A stopped object starts moving. After 3.2 s, it’s moving 18 m/s. The net force acting on it is 328 N. What is its mass?

Explanation:

Speed of sound is 344

The frequency corresponding to the lower cut-off point is the lowest frequency which his 15Hz

F=15Hz

The relationship between the wavelength, speed and frequency is given as

v=fλ

Then,

λ=v/f

λ=v/f

λ=344/15

λ=22.93m

The tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. When the elevator accelerates, the force of acceleration on the package will be equal and opposite to the tension in the string, causing the tension to increase.

The equation for tension in a string is:

Tension = Mass x Acceleration

Therefore, in this case, the tension in the string is equal to 1.85 kg x Acceleration.

If we assume that the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.

To sum up, the tension in the string of a 1.85 kg package held by a light vertical string will depend on the acceleration of the elevator. If the acceleration of the elevator is a constant rate, then the tension in the string can be calculated by multiplying the mass of the package by the acceleration of the elevator.

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The work done by the tension force on Magnus is 2170 J.

What is work?

Work is the product of the force acting on an object and the distance through which the object moves. In other words, work is accomplished when a force is used to transfer energy to an object, causing the object to move some distance as a result.

The force of 1400 N, Distance of 1.55 meters, and a rope tied around Magnus's waist.

The work done by the tension force on Magnus is the product of the force exerted by the tension force and the distance through which Magnus is moved.

W = Fd

where W = Work done by the tension force on Magnus

F = Force of tension force

  = 1400 Nd

  = Distance moved by Magnus

  = 1.55 m

Substituting these values:

W = 1400 N x 1.55 mW

   = 2170 J

Hence, the work done by the tension force on Magnus is 2170 J.

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The formula for the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:

Impulse = (Final momentum - Initial momentum)

Impulse is a vector quantity having both magnitude and direction, whereas momentum is a vector quantity, but the impulse is not equal to momentum. The impulse is the change in momentum.

If a ball of mass m is dropped from rest, then its initial momentum is zero.

The final momentum of the ball after falling for time t is:

Final momentum = mv

Where v is the velocity of the ball after falling for time t.

Therefore, the impulse exerted on the ball from the instant it is dropped to an arbitrary time later is:

Impulse = (mv - 0) = mv

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When a resistor and a capacitor are connected in series across an ideal battery, the voltage across the capacitor is zero at the moment contact is made with the battery.

The correct option is c.

An ideal battery is a voltage source that delivers a constant voltage regardless of the load resistance or current drawn from it.

An ideal battery can maintain a steady voltage regardless of the amount of current being drawn from it.

In real-life batteries, there is always some internal resistance, which causes the voltage to drop as the current increases.

A resistor is an electrical component that opposes or limits the flow of electrical current. It has two terminals and can be made of various materials like carbon, metal, and ceramic. It is used in various applications, including voltage dividers, current limiting, and biasing.

A capacitor is an electronic component that stores energy in an electric field between two charged conductors. It has two terminals and is made of two conducting plates separated by an insulating material called a dielectric.

Capacitors are used in various applications, including energy storage, timing circuits, and power conditioning.

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For a spherical capacitor with a capacitance of 125 and a vacuum between its conducting shells, the outer radius of the inner shell is around 5.60 cm.

The capacitance of a spherical capacitor is given by:

C = 4πε₀[(r₁r₂)/(r₂-r₁)]

where C is the capacitance, ε₀ is the electric constant (8.85 x [tex]10^{-12}[/tex] F/m), r₁ is the radius of the inner shell, and r₂ is the radius of the outer shell.

In this case, we know that the capacitance C = 125 pF (picoFarads), r₂ = 9.00 cm, and we want to find r₁.

We can rearrange the equation to solve for r₁:

r₁ = (C × r₂)/(4πε₀ + C)

Substituting the values:

r₁ = (125 x [tex]10^{-12}[/tex] F × 0.09 m) / (4π × 8.85 x [tex]10^{-12}[/tex] F/m + 125 x [tex]10^{-12}[/tex] F)

r₁ ≈ 5.60 cm

Therefore, the outer radius of the inner shell is approximately 5.60 cm.

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The television commercial loudness increases by 10 decibels.

The decibel (dB) scale is a logarithmic measure of sound intensity. The intensity of a sound is measured in watts per square meter and the decibel scale is a way to express the relative loudness of a sound, compared to a reference level.

A 10 dB increase in intensity is a 10-fold increase in sound power. This means that a sound with an intensity of 10 watts per square meter is 10 times louder than a sound with an intensity of 1 watt per square meter.

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The magnitude of the force per unit length on the wire carrying a current of 4 amps in a magnetic field of 2 Tesla, oriented perpendicular to the wire will be 8 N/m.

It can be determined using the formula F = BIL,

where F is the force per unit length,

B is the magnetic field,

I is the current and

L is the length of the wire.

For the given data, B = 2 T, I = 4 A, L = 1 meter.

Therefore, F = BIL= 2 T x 4 A x 1 m= 8 N/m. Thus, the magnitude of the force per unit length on the wire is 8 N/m.

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According to Ohm's Law, the relationship between the total current and the currents passing through each resistor is that the total current is equal to the sum of the currents passing through each resistor.

This can be represented mathematically as I total = I₁ + I₂ + I₃ + ... where I total is the total current and I₁, I₂, I₃, etc. are the currents passing through each resistor.

This relationship is consistent with Kirchhoff's Current Law, which states that the sum of the currents entering and leaving a junction in a circuit must be equal to zero. Therefore, the current flowing through each resistor must add up to the total current in the circuit. Yes, this relationship is observed in data obtained from circuits.

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If you drop a stone down a well that is 9.5 m deep, it will take approximately 0.028 seconds for you to hear the splash. This is because the speed of sound in air is 343 m/s, and air resistance is negligible.

The question is about finding the time it will take for the sound of the splash to reach the surface of the well. Given data:

Depth of the well = 9.5 m

Speed of sound in air = 343 m/s

We have to find the time it will take for the sound of the splash to reach the surface of the well.

Let's assume that "t" is the time that the sound of the splash takes to reach the surface of the well.

Using the formula:

t  = Distance/Speed

Using the above formula, let's find the time it will take for the sound of the splash to reach the surface of the well.

Distance = Depth of the well = 9.5 m

Speed = Speed of sound in air = 343 m/s

So, the time is:

t = Distance/Speed

t = 9.5/343

t = 0.0277 s ≈ 0.028 s

Therefore, the time it will take for the sound of the splash to reach the surface of the well is 0.028 s

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The positively charged object gains 20 electrons when its charge decreases by 3.2 x 10^-18 C.

What is Positive Charge?

A positive charge is an electrical property of matter that describes the presence of more positively charged protons than negatively charged electrons in an atom or molecule. In other words, an object with a positive charge has lost one or more electrons, resulting in a net charge that is greater than zero.

We know that the charge on a single electron is 1.602 x 10^-19 C.

To calculate the number of electrons gained by a positively charged object when its charge decreases by 3.2 x 10^-18 C, we can use the formula:

number of electrons = (magnitude of charge lost) / (charge on a single electron)

number of electrons = (3.2 x 10^-18 C) / (1.602 x 10^-19 C)

number of electrons = 20

Therefore, the positively charged object gains 20 electrons when its charge decreases by 3.2 x 10^-18 C.

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The minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.

The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),

where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.

For example, if the order of interference is 3, the wavelength of the light is 600 nm, and the index of refraction is 1.4,

the minimum thickness of the film for constructive interference of reflected light would be t = 3*600/(2*1.4) = 850 nm.

Constructive interference of reflected light occurs when the phase difference between the two waves is equal to an integral multiple of 2π.

This can be determined using the formula Δφ = (2π*m)/(λ*n), where Δφ is the phase difference, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.

To achieve constructive interference, the minimum thickness of the film can be determined by ensuring that the phase difference is equal to an integral multiple of 2π.

The minimum thickness of a film required for constructive interference of reflected light can be calculated using the formula t = m*λ/(2*n),

where t is the minimum thickness of the film, m is the order of interference, λ is the wavelength of the light, and n is the index of refraction of the film.

Constructive interference can be achieved by ensuring that the phase difference between the two waves is equal to an integral multiple of 2π.

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The water molecules require more energy to be further separated and converted into steam than it does to convert ice to liquid water, because liquid water has a higher specific heat capacity than ice, which means that it requires more energy to raise its temperature.

In order to convert liquid water into steam, the water molecules must absorb a large amount of energy. This energy is used to overcome the strong intermolecular forces of attraction between the water molecules that hold them in their liquid state. This energy is known as the latent heat of vaporization.

In contrast, when ice is converted into liquid water, the energy required is only enough to overcome the weaker intermolecular forces of attraction that hold the ice in its solid state. This energy is known as the latent heat of fusion.

Once the ice has been converted to liquid water, the water molecules require more energy to be further separated and converted into steam than they did to overcome the weaker forces that held them together as a solid ice block. This is because liquid water has a higher specific heat capacity than ice, which means that it requires more energy to raise its temperature.

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The angular momentum of the ball rotating on the end of a thin string in a circle of radius 1.45 m m at an angular speed of 11.6 rad/s r a d / s is 6.07 × 10⁻⁶ kg m²/s.

Angular momentum is the quantity of motion that describes the rotation of a body about a fixed axis. It is a vector quantity that is the cross product of the position vector and the momentum vector.

The angular momentum of a 0.205 kg k g ball rotating on the end of a thin string in a circle of radius 1.45 m m at an angular speed of 11.6 rad/s r a d / s can be calculated as follows:

L = IωL = Iω

Here, L is angular momentum,

I is the moment of inertia of the ball, and

ω is the angular velocity of the ball.

The moment of inertia of a uniform sphere can be calculated as follows:

I= (2/5)mr²I = (2/5)mr²

Here, m is the mass of the sphere, and r is the radius of the sphere.

Therefore, the moment of inertia of the ball is given by:

I = (2/5)mr²I = (2/5) × 0.205 × (0.00145)²I = 5.23 × 10⁻⁷ kg m²

Substituting this value into the expression for angular momentum:

L = IωL = 5.23 × 10⁻⁷ × 11.6L = 6.07 × 10⁻⁶ kg m²/s.

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Momentum may be demonstrated to be conserved for a properly described system using Newton's third law.

Newton's third law may be used to show that momentum is preserved for a system that is adequately defined. The Earth is being drawn towards the item in an equal and opposing force to that of gravity acting on the object while it is in free fall. As a result, the object's momentum is transferred to the Earth, which has a considerably higher mass and is hence more difficult to detect. The system's overall momentum—that of the Earth and the object—remains preserved. An open system like this one allows momentum to be shared with the environment while yet adhering to conservation standards.

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In an n-type piece of silicon, the electric field causes the electrons to accelerate due to the attractive force between the negatively charged electrons and the positively charged electric field. This acceleration causes the electrons to reach a velocity of V = E/μ, where E is the electric field (0.1V/m) and μ is the mobility of electrons in silicon (1350 cm2/V⋅s). Therefore, the velocity of electrons in this material would be equal to 0.1V/m/1350cm2/V⋅s = 0.0741 cm/s.

The holes, on the other hand, experience a repulsive force due to the positive electric field. This causes the holes to decelerate, with a velocity of V = -E/μ. Therefore, the velocity of holes in this material would be equal to -0.1V/m/1350cm2/V⋅s = -0.0741 cm/s.

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Among the given options, the appliance with the lowest typical energy cost is the microwave oven. Typical energy cost refers to the average amount of money spent on energy usage by an appliance or device over a certain period of time.

Microwave ovens use electromagnetic radiation to cook or heat food, and they are generally more energy-efficient compared to other appliances such as dishwashers, washing machines, and refrigerators. This is because microwave ovens use less power and cook food faster than conventional ovens, reducing energy waste and costs. However, it is important to note that the exact energy cost of an appliance can depend on factors such as its age, model, usage, and energy efficiency rating.

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The magnitude and direction of the net force on the center charge is 3.929 x 10⁻⁴ N.

The unit of charge is the Coulomb (C). It is named after French physicist Charles-Augustin de Coulomb and is defined as the amount of electric charge that flows through a circuit when a current of one ampere flows for one second. One Coulomb is also equivalent to the charge on approximately 6.24 x 10¹⁸ electrons. The Coulomb is one of the seven base SI units (International System of Units) and is used to measure electric charge in physics and engineering.

So, the magnitude of the net force on the center charge is 3.929 x 10⁻⁴ N. Since F12 is directed towards the left, and F23 is directed towards the right, the net force is also directed towards the left. Therefore, the direction of the net force on the center charge is to the left.

According to Coulomb's law to calculate the force exerted by each of the other charges on the center charge, and then add them vectorially.

Let's call the left charge Q1, the center charge Q2, and the right charge Q3.

The force exerted on Q2 by Q1 is given by:

F₁₂ = k * |Q1| * |Q2| / r₁₂²

where k is Coulomb's constant, |Q1| and |Q2| are the magnitudes of the charges, and r₁₂ is the distance between them. Since Q1 is positive and Q2 is negative, the force F₁₂ is attractive and directed towards Q1. Because the distance between them is 2m, we can say:

F₁₂ = 9 x 10⁹ Nm²/C² * |52 x 10⁻⁶ C| * |3.10 x 10⁻⁶ C| / (2m)²

= 3.468 x 10⁻⁴ N (attractive)

The force exerted on Q2 by Q3 is given by:

F₂₃ = k * |Q2| * |Q3| / r₂₃²

where |Q3| is positive, and |Q2| is negative, so the force F23 is repulsive and directed away from Q3. The distance between them is also 2m, so:

F₂₃ = 9 x 10⁹ Nm²/C² * |3.10 x 10⁻⁶ C| * |68 x 10⁻⁶ C| / (2m)²

= 5.383 x 10⁻⁵ N (repulsive)

To find the net force on Q2, we need to add these two forces vectorially. Since they act along the same line, we can simply subtract their magnitudes:

Fnet = |F₁₂| - |F₂₃|

= 3.468 x 10⁻⁴ N - 5.383 x 10⁻⁵N

= 3.929 x 10⁻⁴ N.

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The net force on a 30.0 nc charge located at the origin by two other charges is the vector sum of the forces exerted by the two other charges. The force exerted by the first charge, -50.0 nC located at (-5.0 m, 2.0 m), is given by:

F1 = (k*q1*q2)/r2, where

Therefore,

F1 = (8.99 x 109 N m2/C2)*(-50.0 nc)*(30.0 nc)/(5.3852) = 2.38 x 10-2 N

Similarly, the force exerted by the second charge, 40.0 nc located at (3.0 m, 1.0 m), is given by:

F2 = (k*q1*q2)/r2, where

Therefore,

F2 = (8.99 x 109 N m2/C2)*(40.0 nc)*(30.0 nc)/(3.1622) = 4.58 x 10-2 N

The net force is the vector sum of F1 and F2 and can be calculated as follows:

F net = F1 + F2 = 2.38 x 10-2 N + 4.58 x 10-2 N = 7.00 x 10-2 N

Therefore, the net force on a 30.0 nc charge located at the origin by two other charges is 7.00 x 10-2 N.

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The phases of Venus show that the solar system is in a heliocentric model instead of a geocentric model because the heliocentric model states that the Sun is at the center of the solar system, while the geocentric model states that Earth is at the center of the universe.

The phases of Venus can only be explained in the heliocentric model because the planet is orbiting the Sun.The phases of Venus are an important piece of evidence supporting the heliocentric model proposed by Nicolaus Copernicus. The geocentric model was the widely accepted model of the universe until the 16th century when Copernicus proposed the heliocentric model, which suggested that the Sun is at the center of the solar system and the Earth and other planets orbit around it.

The phases of Venus show that it orbits the Sun and not the Earth because, as it orbits the Sun, different portions of the planet's sunlit side are visible from Earth. This can only occur in a heliocentric model because Venus is between the Earth and the Sun in its orbit, which causes it to pass through phases. Therefore, the phases of Venus are not consistent with a geocentric model, which suggests that Venus orbits the Earth.

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In the metric system, air pressure is measured in pascals. One pascal is equal to a force of one newton per square meter.

Air pressure can be measured using different units. Pascal is a unit of pressure, defined as one newton per square meter. This unit is named after Blaise Pascal, a French mathematician, physicist, and philosopher who made important contributions to the fields of hydrodynamics and hydrostatics.

In the US customary system, air pressure is measured in pounds per square inch (psi), while in the International System of Units (SI), it is measured in pascals (Pa). The unit psi is used to measure pressure in liquids and gases, and it is defined as the amount of pressure exerted by a force of one pound-force per square inch.

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The resultant force of the water on the semi-circular gate on an inclined wall can be calculated using the equations of hydrostatics.

R = √([tex]F1^2 + F2^2 - 2*F1*F2*cos[/tex])α, where 'R' is the resultant force and 'α' is the angle of the wall.

First, determine the pressure of the water at any given point along the gate. To do this, multiply the density of the water, 'ρ', by the acceleration of gravity, 'g', and then the vertical height of the water relative to the gate, 'h', to get the pressure 'p':

p = ρ*g*h

Second, determine the force acting on the gate. This is done by multiplying the pressure with the area of the gate, 'A':

F = p*A

Finally, find the resultant force, 'R', by adding the forces together and taking into account the angle of the wall:

R = √([tex]F1^2 + F2^2 - 2*F1*F2*cos[/tex])α

where α is the angle of the wall.

By following these steps, you can calculate the resultant force of the water on the semi-circular gate on an inclined wall.

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1 - Since electrοns can be transferred frοm οur hair tο the ballοοn , electrοns cannοt be transferred frοm ballοοn tο οur hair because. This is an illustratiοn οf  charging by cοnductiοn.

2 - Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.

3 - Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.

A charged οbject must cοme intο cοntact with a neutral οbject tο cοnduct electricity. As a result, when twο charged cοnductοrs cοme intο cοntact, the charge is split between the twο cοnductοrs, charging the uncharged cοnductοr.

When twο neutral οbjects are rubbed against οne anοther, electrοns are transferred. The οbject that has a strοnger affinity fοr electrοns will take electrοns frοm the οther οbject, and the twο becοme charged in οppοsitiοn. In this instance, the electrοns frοm the hair are taken up by the ballοοn , which nοw has an excess οf electrοns and a negative charge cοmpared tο the hair's current electrοn shοrtage and pοsitive charge.

2- Since the rubber οn the ballοοn is significantly less cοnductive than the hair, electrοns will nοt easily escape the ballοοn because οf this.

3- Neutrοns are electrically neutral , neutrοns dοesn't participate in this prοcess.

4-Insulating materials may becοme electrically charged when they cοme intο cοntact with οne anοther. Negatively charged electrοns can "rub οff" οne material and "rub οn" tο anοther. After bοth things have the same quantity οf οppοsite charges, the substance that gets electrοns becοmes negatively charged, and the material that lοses electrοns becοmes pοsitively charged.

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The seesaw moved when a third person pushed down on one side. This is because the seesaw is a simple machine that consists of a long plank balanced in the middle with a pivot point that allows it to move up and down.

When the two students sit on the seesaw in a way that makes it balance and not move, they are evenly distributed on each end. However, when the third person pushes down on one side, this distribution of weight becomes unequal, and the seesaw moves in the direction of the heavier side.

The heavier end of the seesaw moves down while the lighter end moves up. This is because the heavier side creates more force, or torque, on the pivot point, causing the seesaw to tilt towards that side.

As a result, the seesaw moves and is no longer in balance.

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Answer: The rock's speed as it left your hand was 8.8 m/s.

Explanation: The system is the rock and the Earth. The initial state is the rock at rest in your hand 2.8 m below the Frisbee. The final state is the rock hitting the Frisbee at a speed of 4.0 m/s.

Using conservation of energy, we know that the initial potential energy of the rock-Earth system is transformed into both kinetic energy and potential energy at its maximum height. Therefore, we can use the conservation of energy equation:

potential energy (initial) = kinetic energy (final) + potential energy (final)

mgh = 1/2mv^2 + mgh

where m is the mass of the rock, g is the acceleration due to gravity, h is the height that the rock has been raised, and v is the velocity of the rock.

We can solve for the initial velocity by rearranging the equation:

v = sqrt(2gh + v^2)

Plugging in the values, we get:

v = sqrt(2 * 9.81 * 2.8 + 4^2)

v ≈ 8.8 m/s

Therefore, the rock's speed as it left your hand was 8.8 m/s.

A brick is falling from the roof of three story building then free-body diagram would show only one force vector, which is the force of gravity acting on the brick.

A free-body diagram is used to graphically represent the forces acting on an object. It shows all of the forces acting on an object and can be used to analyze the motion of an object.

A free-body diagram for a falling brick would include two force vectors: Gravity or Weight.

So, in this scenario, the free-body diagram would show only one force vector, which is the force of gravity acting on the brick.

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Answer: the answer given below

(a) Explanation: The impulse on an object is given by the change in momentum of the object. Before the collision, the bullet has momentum p1 = mv0 and the brick has momentum p2 = 0, since it is stationary. After the collision, the combined bullet-brick system has momentum p3.

Conservation of momentum requires that the total momentum before the collision is equal to the total momentum after the collision:

p1 + p2 = p3

mv0 + 0 = (m + M)V

where V is the velocity of the combined bullet-brick system after the collision. Solving for V, we get:

V = (mv0) / (m + M)

The impulse on the bullet during the collision is equal to the change in momentum of the bullet:

J_bullet = p3 - p1 = (m + M)V - mv0

Substituting the expression for V we found earlier:

J_bullet = (m + M)(mv0) / (m + M) - mv0 = 0

Therefore, the impulse on the bullet is zero during the collision.

On the other hand, the impulse on the brick during the collision is:

J_brick = p3 - p2 = (m + M)V - 0 = (m + M)(mv0) / (m + M) = mv0

Therefore, the magnitude of the impulse acting on the brick is equal to the initial momentum of the bullet, mv0, and it is in the same direction as the initial velocity of the bullet.

In summary, during the collision of the bullet and the brick, the impulse acting on the bullet is zero, while the impulse acting on the brick is mv0 in the direction of the initial velocity of the bullet.

(b) We can use the principle of conservation of momentum to solve for the velocity of the brick-bullet combination just after the collision. The total momentum of the system (bullet, brick, and Earth) is conserved before and after the collision. Initially, only the bullet has momentum, which is given by p1 = m*v0, and the momentum of the brick and Earth is zero. After the collision, the bullet becomes embedded in the brick, and the combined system of the brick-bullet has momentum p2. Since the momentum of the Earth is negligible compared to that of the bullet and brick, we can treat the system as closed and apply conservation of momentum:

p1 = p2

m*v0 = (M + m)*v

where v is the velocity of the combined system just after the collision.

Solving for v, we get:

v = (m*v0) / (M + m)

Therefore, the magnitude of the velocity of the brick-bullet combination just after the collision is:

|v| = |(m*v0) / (M + m)|

The direction of the velocity is upward, as the system swings up after the collision due to the conservation of momentum.

(c) The initial kinetic energy of the system is the kinetic energy of the bullet just before the collision, which is given by:

KE1 = (1/2)mv0^2

The final kinetic energy of the system is the kinetic energy of the combined brick-bullet system just after the collision, which is given by:

KE2 = (1/2)*(M + m)*v^2

Substituting the expression we found for v:

KE2 = (1/2)(M + m)[(mv0) / (M + m)]^2

KE2 = (1/2)(m*v0^2) / (1 + M/m)

The ratio of the final kinetic energy to the initial kinetic energy is:

KE2 / KE1 = [(1/2)(mv0^2) / (1 + M/m)] / [(1/2)mv0^2]

KE2 / KE1 = 1 / (1 + M/m)

Therefore, the ratio of the final kinetic energy of the brick-bullet combination immediately after the collision to the initial kinetic energy of the brick-bullet combination is:

KE2 / KE1 = 1 / (1 + M/m)

(d)To determine the maximum vertical position reached by the brick-bullet combination, we can use conservation of energy, assuming there is no energy loss due to friction or other dissipative forces. At the maximum height, the kinetic energy of the system is zero, and all the initial kinetic energy has been converted to potential energy due to the height above the initial position.

The initial total energy of the system is the sum of the initial kinetic energy of the bullet and the gravitational potential energy of the brick:

E1 = (1/2)mv0^2 + Mgh1

where h1 is the initial height of the brick above the ground, and g is the acceleration due to gravity.

At the maximum height, the final total energy of the system is the potential energy due to the height above the ground:

E2 = (M + m)gh2

where h2 is the maximum height reached by the brick-bullet combination above the initial position.

Since there is no energy loss, we can set the initial energy equal to the final energy:

E1 = E2

Substituting the expressions for E1 and E2 and solving for h2, we get:

(M + m)gh2 = (1/2)mv0^2 + Mgh1

h2 = [(1/2)mv0^2 + Mgh1] / [(M + m)*g]

Simplifying, we get:

h2 = (1/2)v0^2 / g + h1(M/m) / (1 + M/m)

Therefore, the maximum vertical position above the initial position reached by the brick-bullet combination is:

h2 = (1/2)v0^2 / g + h1(M/m) / (1 + M/m)

Hope this helps :)

The average force on the person if they are stopped by an airbag that compresses an average of 15.0 cm is approximately 70,000 N.

To calculate the average force on a person,

Average force = (change in momentum) / (time interval)

Assuming that the person's initial velocity is constant, we can simplify the formula to,

Average force = (mass of the person) x (change in velocity) / (time interval)

Now, let's consider the two scenarios,

Stopped by a padded dashboard that compresses an average of 1.00 cm:

Assuming the person's initial velocity is known and constant, we need to know the time interval it takes for the person to stop after hitting the dashboard. Without this information, we cannot calculate the average force.

Stopped by an airbag that compresses an average of 15.0 cm:

The time interval for an airbag to deploy and cushion the person's impact is typically very short (about 0.03 seconds), so we can assume that the time interval is negligible in this case. Therefore, we can use the simplified formula above.

Let's assume the mass of the person is 70 kg and their initial velocity is 30 m/s. The change in velocity is the final velocity (0 m/s) minus the initial velocity (30 m/s), which is -30 m/s. The negative sign indicates that the person's velocity is decreasing.

Using the formula,

Average force = (mass of the person) x (change in velocity) / (time interval)

= (70 kg) x (-30 m/s) / (0.03 s)

= -70,000 N

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The magnitude of the force that Alice is applying to the box is 110 N.

To calculate the force that Alice is applying, we need to use the equation F = ma. In this equation, F is the force applied, m is the mass of the box, and a is the acceleration of the box.

Since Alice is pushing the box at a constant speed of 2.8 m/s, the acceleration is 0, and the equation simplifies to F = 0 x m. Since the force must equal 0 when the acceleration is 0, the magnitude of the force that Alice is applying to the box is 0.

However, since Bob is pushing an identical box across the floor at a constant speed of 1.4 m/s, the acceleration is 0 and the equation simplifies to F = m x a. In this case, a is the acceleration of the box, which is 1.4 m/s.

Since we know that the magnitude of the force Bob is applying is 55 N, we can use the equation to calculate the force Alice is applying. 55 N = m x 1.4 m/s, which simplifies to m = 39.286.

We then substitute m back into the equation F = ma, so F = 39.286 x 1.4 m/s. This simplifies to F = 55.0 N, so the magnitude of the force Alice is applying is 55.0 N.

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