When tension is applied to an aluminum rod (Y = 70 x 10^9 Pa) of length 1 m, it stretches by Δ.

1. If the same tension is applied to another aluminum rod with the same cross-sectional area, but of length 2 m, by how much will it stretch?

a) less than Δ
b) Δ
c) more than Δ

2. Now, consider two aluminum rods of length 1 m, one twice as thick as the other. If a compressive force F is applied to both rods, their lengths are reduced by Δthick rod
and Δthin rod, respectively.
The ratio (Δthick rod)/(Δthin rod) is

a) (Δthick rod)/(Δthin rod) < 1
b) (Δthick rod)/(Δthin rod) = 1
c) (Δthick rod)/(Δthin rod) > 1

When an item must be moved 36 meters in 14 seconds using 726 watts of electricity, its mass is 28.8 kg.(c) is the right option.

Any quantity in mechanics may be defined in terms of mass, length, length time. The letter m stands for kilogram, which represents mass in the SI. Contrary to popular belief, relativistic mass must always be thought of when moving at speeds that are near to the lightest possible speed.

The Power is provided with p = 726 watt.

The Time is 14 seconds.

d = 36 m is the distance traveled.

Use the provided formula to calculate power.

p = W / t

p = m * g * h / t (w = m * g * h)

726 = m * 9.8 * 36 / 14 ( g = 10 m/s^2)

m = 28. 8kg.

As a result, the object's mass 36 m in 14 s equals 28.8 kg even when an item needs 726 watts of electricity to move it.

The mass of it as an item, a key indication of the volume of both the thing's contents, is used to calculate its inertia, a fundamental attribute. Descriptions of weight might appear circular because it's such a fundamental concept and difficult to express in words of every other concept.

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(I) The focal length of the lens is 180.0 cm.

(II) The distance for which the image would be the same size as the object is 90.0 cm.

We can use the lens equation and the magnification formula to solve for the focal length of the lens and the distance for which the image would be the same size as the object.

The lens equation is:

1/f = 1/do + 1/di

where;

We are given that the distance between the image and the object is 90.0 cm and the magnification is 2. The magnification formula is:

m = - di/do

where;

Substituting these values into the magnification formula, we get:

2 = - di/do

di = -2do

Substituting these values into the lens equation, we get:

1/f = 1/do - 1/2do

Simplifying this equation, we get:

1/f = 1/2do

f = 2do

Substituting the given value of di, we get:

f = 2(-90.0 cm) = -180.0 cm

Since the focal length must be positive for a converging lens, we take the absolute value and get:

f = 180.0 cm

(ii) Distance for which the image would be the same size as the object:

When the image is the same size as the object, the magnification is 1. We can use the magnification formula to solve for the distance di:

m = - di/do

1 = - di/do

di = -do

Substituting the given value of do, we get:

di = -90.0 cm

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The color of an object has to do with the light wavelength. A white t-shirt looks yellow because it absorbs all the colors while black white all the wavelengths of light. A ripe mango is yellow because reflect all the reflects wavelengths.

The light wavelength has an impact on an object's color of which the object reflects. Because it absorbs all hues, a white t-shirt seems yellow, but a black one emits all light wavelengths. A ripe mango appears yellow because, when white light strikes it, its atomic impurities bounce all the wavelengths of light at our sight more than the other colors. ​

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The distance an object travels in a unit of time is called the speed of the object. SI. the unit of speed is meter per second (ms−1).

Speed ​​is measured in relation to distance compared to the time it took to cover the distance. Speed ​​is a scalar quantity because it only has  direction and not magnitude.  There are four types of speeds and they are:

Even speed
Variable speed
Average speed
Instantaneous speed
Constant velocity: An object is at a constant velocity when the object travels the same distance in equal intervals of time.
Variable speed: an object is said to have variable speed when the object travels varying distances at regular intervals.
Average speed: Average speed is defined as the constant speed obtained by the ratio of the total distance traveled by the object to the total time spent on the object.  Instantaneous velocity: When an object is moving with a variable velocity, the velocity of that object at any instant of time is called instantaneous velocity.
Speed ​​measurement
A speedometer is used to measure the speed of vehicles. An odometer is used to measure the distance traveled. Speed ​​can also be calculated using a gragraphph. A distance-time graph helps to understand the speed of an object.

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The speed of the sled and the two people immediately after the collision is approximately 15.8 m/s.

The conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the sled and the two people form a closed system, because there are no external forces acting on them.

Let's define the initial state as before the collision, and the final state as after the collision. In the initial state, the sled and the 76 kg person have a momentum of:

p1 = (76 kg)(20 m/s) = 1520 kg·m/s

The second person is stationary, so their momentum is zero:

p2 = 0 kg·m/s

The total momentum before the collision is therefore:

p1i = p1 + p2 = 1520 kg·m/s + 0 kg·m/s = 1520 kg·m/s

In the final state, the two people and the sled move together with a common velocity, which we'll call v. The total mass of the system is:

m = 76 kg + 20 kg = 96 kg

The total momentum after the collision is:

p1f = m v

By the conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision:

p1i = p1f

1520 kg·m/s = 96 kg × v

Solving for v, we get:

v = 1520 kg·m/s / 96 kg ≈ 15.8 m/s

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Answer:

yes if you can only install a magnetic force into the bar

The speed of the wave remains unchanged.

The speed of a wave is determined by the product of its wavelength and frequency. This can be represented by the formula: speed = wavelength x frequency

If the frequency of a wave is doubled while the wavelength remains the same, then the product of the wavelength and frequency will remain constant. This means that the speed of the wave will also remain constant.

To understand this, let's consider an example:

Suppose the original frequency of a wave is f, and its wavelength is λ. Then, the speed of the wave is given by:

speed = λ x f

Now, if the frequency is doubled, the new frequency becomes 2f. The wavelength remains the same at λ. So, the new speed of the wave can be calculated as: new speed = λ x 2f = 2(λ x f) = 2 x speed

As we can see, the new speed is twice the original speed, which contradicts our assumption that the speed remains constant. Therefore, the speed of the wave remains unchanged when the frequency is doubled while the wavelength remains the same.

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The tension T in the string just after the objects are released must be equal and opposite to the accelerations of each mass.

The statement refers to a physical principle known as Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

In the context of the given statement, it means that the tension (T) in the string, which is the force transmitted through the string, must be equal in magnitude and opposite in direction to the accelerations of each mass.

When objects are released and allowed to move under the influence of gravity, they may be connected by a string or rope. As the objects accelerate due to the force of gravity, the tension in the string changes to keep the objects connected and moving together.

According to Newton's third law, the tension in the string must be equal and opposite to the accelerations of each mass.

If one of the objects has a greater acceleration, the tension in the string must be higher on that side to counteract the greater acceleration.

Similarly, if one of the objects has a lower acceleration, the tension in the string must be lower on that side. This ensures that the net force on each object is balanced and that they move together without breaking the string.

This is because Newton's Second Law states that the sum of the forces on an object is equal to the mass times the acceleration: F = ma. Therefore, the tension T must be the same for both masses, since their accelerations must be equal and opposite.

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(a) To find the truck's velocity relative to you, we need to subtract your velocity from the truck's velocity.

Since you are driving north and the truck is approaching you in the other lane, the velocities are in opposite directions. Therefore, we can simply subtract the two speeds: Truck's velocity relative to you = Truck's velocity - Your velocity = 104 km/h - 88 km/h = 16 km/h north (since the truck is approaching you). Therefore, the truck's velocity relative to you is 16 km/h north. (b) To find your velocity relative to the truck, we need to subtract the truck's velocity from your velocity. Since you are driving north and the truck is approaching you from the opposite direction, the velocities are again in opposite directions. Therefore, we can simply subtract the two speeds: Your velocity relative to the truck = Your velocity - Truck's velocity = 88 km/h - 104 km/h = -16 km/h north (since you are moving away from the truck). Therefore, your velocity relative to the truck is 16 km/h south. (c) After you and the truck pass each other, the relative velocities change. The truck is now moving away from you, and you are moving away from the truck. Therefore, the velocity of the truck relative to you will decrease, while your velocity relative to the truck will increase. However, the magnitude of the relative velocities will remain the same, since the difference between the two velocities is still 16 km/h. The direction of the relative velocities will also change, with the truck's velocity relative to you now being 16 km/h south, and your velocity relative to the truck now being 16 km/h north.

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For Machine 1  ideal mechanical advantage is 4, for machine 2 the IMA is 8 and for the machine 3 the IMA is 4. The load the machines can lift is 400N, 800N and 200N respectively.

The ideal mechanical advantage of a machine is an important factor in determining its efficiency and usefulness. The higher the IMA, the easier it is to lift heavy loads with less effort. However, it is important to note that the actual mechanical advantage (AMA) may differ from the ideal due to various factors such as friction and other mechanical losses. Therefore, it is essential to consider both IMA and AMA when evaluating the performance of a machine.

Machine 1:

Ideal Mechanical Advantage (IMA) = Load / Effort

IMA = 400 N / 100 N

= 4

Machine 2:

IMA = Load / Effort

IMA = 800 N / 100 N

= 8

Machine 3:

IMA = Load / Effort

IMA = 200 N / 50 N

= 4

In simple terms, the ideal mechanical advantage (IMA) of a machine is the ratio of the load it can lift to the effort or force needed to lift it. In other words, it is the number of times a machine multiplies the force or effort applied to it.

For Machine 1, the IMA is 4, which means that the machine can lift a load that is four times heavier than the applied force. Therefore, if you apply 100 N of force to the machine, it can lift a load of up to 400 N.

For Machine 2, the IMA is 8, which means that it can lift a load that is eight times heavier than the applied force. If you apply 100 N of force to this machine, it can lift a load of up to 800 N.

For Machine 3, the IMA is 4, which means that it can lift a load that is four times heavier than the applied force. If you apply 50 N of force to this machine, it can lift a load of up to 200 N.

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The magnitude of the induced emf if magnetic field is reduced to zero in 0.12 seconds is 14.058 V.

The emf induced in a circular loop of wire is given by Faraday's law of electromagnetic induction:

emf = - N * (dΦ/dt)

where N is the number of turns in the loop,

Φ is the magnetic flux through the loop, and

(dΦ/dt) is the rate of change of magnetic flux through the loop.

The circular loop has a radius of 15 cm and consists of 53 turns of wire.

The magnetic field passing through the loop is perpendicular to its plane and has a magnitude of 0.45 T. The magnetic field is reduced to zero in 0.12 s.

The magnetic flux through the circular loop is given by:

Φ = B * A

where B is the magnetic field, and

A is the area of the circular loop.

Since the magnetic field is perpendicular to the plane of the loop, the area A is given by:

A = π * r²

where r is the radius of the circular loop.

Substituting the given values, we get:

A = π * (0.15 m)²= 0.0707 m²

Φ = B * A = (0.45 T) * (0.0707 m²) = 0.0319 Wb.

The rate of change of magnetic flux through the loop is given by:

(dΦ/dt) = -ΔΦ/Δt

where ΔΦ is the change in magnetic flux and

Δt is the time taken for the change.

Substituting the given values, we get:

(dΦ/dt) = -Φ/Δt = -(0.0319 Wb) / (0.12 s) = -0.266 Wb/s

Finally, substituting the values of N and (dΦ/dt) in Faraday's law, we get:

emf = - N * (dΦ/dt) = -(53) * (-0.266 V) = 14.058 V

Therefore, the magnitude of the induced emf in the circular loop is 14.058 V.

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Answer:

50m/s.

Explanation:

Answer:

[tex]V_f=50m/s[/tex]

Explanation:

Use the the formula for final velocity (kinematic equation):

[tex]V_f=V_i+at[/tex]

Final velocity = Initial velocity + acceleration times time

Given values:

Rest - indicates 0 initial velocity

Acceleration - 10 m/s^2

Time - 5 seconds

Insert the given values:

[tex]V_f=0+5\times10[/tex]

[tex]V_f=50m/s[/tex]

The impulse that acts on the shoe during its collision with the wall is -15 kg*m/s (to the left).

Calculation steps:

The initial momentum of the shoe, p1 = mv1 = 0.3 kg * 20 m/s = 6 kgm/s (to the right)

The final momentum of the shoe, p2 = mv2 = 0.3 kg * (-30 m/s) = -9 kgm/s (to the left)

The change in momentum, Δp = p2 - p1 = -9 kgm/s - 6 kgm/s = -15 kg*m/s (to the left)

Therefore, the impulse acting on the shoe during its collision with the wall is J = Δp = -15 kg*m/s (to the left)

What is impulse?

Impulse refers to the change in momentum of an object when a force is applied to it for a certain amount of time. It is defined as the product of the force and the time for which it acts on an object. Mathematically, impulse can be expressed as:

J = F * Δt

where J is the impulse, F is the force applied, and Δt is the time for which the force acts.

What is momentum?

Momentum is a physical quantity that measures the motion of an object. It is defined as the product of an object's mass and velocity. In other words, momentum = mass x velocity.

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The mass of the planet is approximately [tex]7.87 x 10^23 kg.[/tex]

We can use the formula for the gravitational force between two masses:

[tex]F = G * (m1 * m2) / r^2[/tex]

where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. In this case, the person's weight on the planet is equal to the force of gravity between the person and the planet: F = 75 N. The person's mass is 80 kg, so their weight on Earth would be:

[tex]W = m * g = 80 kg * 9.8 m/s^2 = 784 N[/tex]

We can set these two forces equal to each other and solve for the mass of the planet: [tex]75 N = G * (80 kg * m_planet) / (r_planet)^2\\[/tex]We can rearrange this equation to solve for the mass of the planet:

[tex]m_planet = (75 N * (2500 km)^2) / (G * 80 kg)\\[/tex]

where[tex]G = 6.674 x 10^-11 N*m^2/kg^2[/tex]is the gravitational constant.

Plugging in the values, we get: m_planet = [tex](75 N * (2500 km)^2) / (6.674 x 10^-11 N*m^2/kg^2 * 80 kg)[/tex]

m_planet = [tex]7.87 x 10^23 kg[/tex]

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The magnitude of the total displacement of Olivia's trip is 1.9 miles. The direction of the total displacement of her trip is southeast.

To find the magnitude of the total displacement, we need to use the Pythagorean theorem:
a^2 + b^2 = c^2

In this case, a = 0.9 miles (the distance she travels south), and b = 0.8 + 1.4 = 2.2 miles (the distance she travels east).

Plugging in these values, we get:
0.9^2 + 2.2^2 = c^2
0.81 + 4.84 = c^2
5.65 = c^2
c = √5.65
c = 2.376

So the magnitude of the total displacement is approximately 2.376 miles.

To find the direction of the total displacement, we need to use the tangent function:
tan θ = opposite/adjacent

In this case, opposite = 2.2 miles (the distance she travels east), and adjacent = 0.9 miles (the distance she travels south).

Plugging in these values, we get:

tan θ = 2.2/0.9
θ = tan^-1(2.2/0.9)
θ = 67.38 degrees

So the direction of the total displacement is approximately 67.38 degrees from south, or southeast.

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The following are the answers to the following questions:

There will not be a Doppler shift.

There will still be a Doppler shift observed by the radar gun.

Doppler shift is the change in frequency of a wave caused by relative motion between the source and the observer. This shift in frequency can be used to calculate the relative motion of the source and observer and is employed in a variety of applications such as radar, astronomy, and medical imaging.

1: The guns are adjusted for forward or backward motion towards or away from the gun. What happens if an automobile moves perpendicular to the gun's line of sight?

The radar gun will not detect any Doppler shift.

2: If the car is approaching or departing from a different angle, there is .

A Doppler change will still be detected, but it will be less than the maximum Doppler shift that would occur if the car moved directly towards or away from the gun.

3: As a result, if the radar gun indicates that a car is driving at a specific speed, the car is moving at the speed radar report.

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The current moving through a wire that has 0. 60 C of electrons passing through a point in 1. 5 min is  0.4 Amps (A).

The current is 0.4 Amps (A),

It is calculated using the formula

I = Q/t,

  = 0.60/1.5

  = 0.4 Amps

where Q is the charge (Coulombs) of electrons and t is the time (seconds) taken for them to pass through the point.

The positive sign for current corresponds to the direction a positive charge would move. In metal wires, current is carried by negatively charged electrons, so the positive current arrow points in the opposite direction the electrons move.

In fact, an electric current is defined as the net movement of charge(s). This includes slow drift of electrons inside a wire, or a stream of electrons, protons, or muons traveling near light speed through the vacuum inside a particle accelerator.

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A boat float on the surface of the lake sends a signal summer force vertically down to the water the sooner trace is 0. 007 sand the speed of sound is 1,500m/s. 21 meters deep is the water.

The time it takes for the sound wave to travel from the boat to the bottom of the lake and back is given by:

t = 2d/v

Where:

d = depth of the water

v = speed of sound in water (1,500 m/s)

We can solve for d by rearranging the equation as:

d = v × t/2

Where:

t = the time it takes for the sound wave to travel from the boat to the bottom of the lake and back, which is equal to twice the time it takes for the sound wave to travel from the boat to the bottom of the lake.

The time it takes for the sound wave to travel from the boat to the bottom of the lake is given by:

t = d/v

Where:

d = distance traveled by the sound wave (which is equal to the depth of the water)

v = speed of sound in water (1,500 m/s)

We can substitute this expression for t into the equation for d to get:

d = v × d/2v

Simplifying this expression, we get:

d/0.007 = 2 × 1500

d = 21 meters

Therefore, the depth of the water is approximately 21 meters.

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The electrostatic force each charge exerts on the other is  2.81N  .[tex]q_{1} =[/tex] [tex]3[/tex] × [tex]10^{-6} C[/tex][tex]\\q_2}[/tex]  [tex]= - 1.5[/tex] × [tex]10^{-6} C[/tex]   They are separated by a distance [tex]r = 0.12m[/tex]

Electrostatic force is [tex]F =[/tex] [tex]\frac{kq_{1} q_{2} }{r^{2} }[/tex]

[tex]F = 2.81N[/tex]

The term "scalar" refers to a category of quantities that may be fully defined by a single magnitude. Quantities called vectors can be fully represented by their direction as well as their magnitude.

How do you define a vector's magnitude?

A vector's length is considered to be its magnitude. The letter "a" stands for the dynamic array magnitude. For further information about a vector's magnitude, go to its introduction. This article deduces formulas for vectors magnitude in considerations of their coordinates in three and two dimensions, respectively.

Magnitude is simply "distance or amount," according to the definition given in physics. It illustrates the either the absolute or relative size or velocity direction for an item.

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Answer:

MCB (Miniature Circuit Breaker) is generally considered better than fuses for several reasons:

Cost-effective: MCBs are more cost-effective in the long run compared to fuses as they can be reset and reused after tripping, whereas fuses need to be replaced each time they blow.

Convenience: MCBs can be reset with the flip of a switch, while fuses need to be manually replaced, which can be a hassle.

Accuracy: MCBs are more accurate in protecting against overloading and short circuits. They can be set to trip at specific amperages, providing better protection against damage to electrical appliances and wiring.

Safety: MCBs are safer than fuses as they do not produce arc flashes during tripping, which can cause electrical fires or explosions.

Overall, MCBs are a more efficient and safer alternative to fuses for protecting electrical circuits.

Explanation:

To calculate time, divide the distance by speed.  hence, the time is 7.5 minutes.

Divide the distance by the speed to find the passing duration. Multiply the speed by the duration to get the distance. These formulae can be represented more simply as s=d/t, where s stands for speed, d for distance, and t for time.
Given: speed= 50 mph.
distance= 10km
1 mile = 1.6 km
1km = 1/1.6 miles= 0.625 milesmiles
We know that, time= distance/speedspeed
Time = 0.625*10/50= 0.125 hours.
1 hour = 60 minutes

hence, 0.125 hours= 60*0.125 = 7.5 minutes.

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Answer:

B. herbivore.

Explanation:

Meadow voles primarily consume plants, such as grasses, herbs, and bark, although they may also eat insects occasionally. As a result, their niche in an ecosystem is that of a herbivore, which is an organism that consumes primarily plants.

When two rope segments pull up on the load in the single movable pulley, the optimal mechanical advantage is 2. This sort of pulley does not change the direction of the applied force, but it does increase it by a factor of two.

There are two methods for calculating a pulley system's mechanical advantage.

The mechanical advantage may be calculated simply by counting the number of falls (or active lifting ropes) that are really attached to the load. You may also split the effort distance by the load distance.

Assuming an ideal rope and pulley system with a mechanical advantage of  [tex]2.00[/tex] , the output load that can be lifted with an input force of [tex]200 N[/tex] can be calculated using the formula:

Output force = Input force x Mechanical advantage

Where the mechanical advantage is given as [tex]2.00[/tex]  .

Thus, the output force is:

Output force [tex]= 200 N \times 2.00 = 400 N[/tex]

Therefore, with an input force of [tex]200 N[/tex]  , the rope and pulley system can lift an output load of up to [tex]400 N[/tex] .

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Metamorphosis refers to the process of development and change in the body form of certain animals as they grow from juveniles to adults.

Explain the types of metamorphosis?

Metamorphosis is classified into two types: complete and incomplete.

1. Complete metamorphosis:

Complete metamorphosis is a developmental process in which the juvenile form of an animal goes through four distinct stages: egg, larva, pupa, and adult. In this type of metamorphosis, the juvenile form looks completely different from the adult form in terms of appearance, behavior, and habitat.

Animals that undergo complete metamorphosis include:

a) Butterflies and moths: The egg hatches into a caterpillar (larva) that feeds and grows rapidly. The larva then forms a pupa or chrysalis, where the body undergoes a complete transformation into an adult butterfly or moth.

b) Flies: The egg hatches into a worm-like maggot (larva) that feeds and grows. The maggot then transforms into a pupa, and finally, an adult fly emerges.

c) Beetles: The egg hatches into a grub (larva) that feeds and grows. The grub then transforms into a pupa, and finally, an adult beetle emerges.

Incomplete metamorphosis:

Incomplete metamorphosis is a developmental process in which the juvenile form (nymph) of an animal resembles the adult in appearance and habitat, but is smaller and lacks wings. The nymph goes through several stages of growth and molting before reaching adult form.

Animals that undergo incomplete metamorphosis include:

a) Grasshoppers: The egg hatches into a nymph that resembles the adult grasshopper but lacks wings. The nymph goes through several molts and growth stages before developing wings and reaching the adult stage.

b) Cockroaches: The egg hatches into a nymph that resembles the adult cockroach but lacks wings. The nymph goes through several molts and growth stages before developing wings and reaching the adult stage.

c) Dragonflies: The egg hatches into a nymph that lives in water and resembles the adult dragonfly but lacks wings. The nymph goes through several molts and growth stages before developing wings and emerging from the water as an adult dragonfly.

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A-the minimum coefficient of friction is 0.18 ,B- it is unreasonable, C-no premises is inconsistent.

(a) Calculation of the minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s:  A car moving with a velocity of 30.0 m/s in a circular path of radius 50.0 m negotiates an unbanked curve. Hence, the force required to move a car in a circular path is the frictional force between the wheels of the car and the road.

The minimum coefficient of friction needed for a car to negotiate an unbanked 50.0 m radius curve at 30.0 m/s is given by:μmin = tanθ= v² / rgWhere,μmin is the minimum coefficient of frictionv is the velocity of the carr is the radius of the curveg is the acceleration due to gravity θ is the angle of banking.

As the curve is unbanked, the angle of banking is 0°.∴ μmin = v² / rg= (30.0 m/s)² / (50.0 m × 9.81 m/s²)= 0.183 or 0.18 (approx)

(b)The result of 0.18 is not unreasonable.

(c) None of the premises is unreasonable or inconsistent.

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The correct answer for a) the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off, b) rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, c) the boosters were firing for 58.04 seconds, d)  the rocket is in the air for a total of 199.38 seconds

a) To find the distance from the ground when the boosters turned off, we can use the formula for displacement in terms of initial velocity, acceleration, and time:
d = v_i*t + 0.5*a*t^2

We know the initial velocity (v_i) is 0 m/s, the acceleration (a) is 11.7 m/s^2, and the final velocity (v_f) is 679 m/s.

We can use the formula v_f = v_i + a*t to find the time (t) that the boosters were firing:

679 m/s = 0 m/s + 11.7 m/s^2 * t

t = 58.04 s

Now we can plug this time into the displacement formula:

d = 0 m/s * 58.04 s + 0.5 * 11.7 m/s^2 * (58.04 s)^2

d = 19,671.65 m

So the rocket was 19,671.65 meters (or 19.67 km) from the ground when the boosters turned off.

b) The prototype rocket's upward acceleration while its boosters were firing was 11.7 m/s^2, as given in the question.

c) As calculated in part a), the boosters were firing for 58.04 seconds.

d) To find the total time the rocket is in the air, we need to find the time it takes to reach its maximum height and the time it takes to fall back to the ground.

We can use the formula d = v_i*t + 0.5*a*t^2 again, with the initial velocity (v_i) being 679 m/s, the acceleration (a) being -9.8 m/s^2 (due to gravity), and the displacement (d) being the difference between the maximum height and the height when the boosters turned off:

42.3 km - 19.67 km = 22.63 km = 22,630 m

22,630 m = 679 m/s * t + 0.5 * -9.8 m/s^2 * t^2

Solving this quadratic equation gives us two solutions for t, but only one is positive:

t = 70.67 s

So the time it takes to reach the maximum height is 70.67 seconds.

The time it takes to fall back to the ground is the same, since the initial and final velocities are the same but in opposite directions. Therefore, the total time the rocket is in the air is:

t_total = 58.04 s + 70.67 s + 70.67 s = 199.38 s

So the rocket is in the air for a total of 199.38 seconds before striking the ground.

To know more about acceleration, refer here:

https://brainly.com/question/28164989#

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