three objects a b c are placed 0.50 m apart along a straight line. If a and b have equal masses of 10.0kg and c has a mass of 15.0kg, what is the net gravitational force on b due to a and c?

More information is needed to be able to answer questions 1 and 3. The knowledge of 'ole" would help to tell that the word arteriole refers to a small  component.

Knowing that the suffix "-ole" means "small or little" would help in defining the term "arteriole". An arteriole is a small or little artery that branches out from an artery and leads to a capillary.

The suffix "-ole" in "arteriole" indicates that it is a small or little version of an artery, which is a larger blood vessel that carries blood away from the heart to other parts of the body.

Therefore, understanding the meaning of the suffix "-ole" helps in breaking down the term "arteriole" into its component parts and understanding its meaning.

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(a) Increasing the reheat in a simple, ideal Rankine cycle with a constant mass flow rate will result in an increase in pump power input. (b) Increasing the reheat in a simple, ideal Rankine cycle with a constant mass flow rate will result in a decrease in turbine power output.
(c) Heat input required increases due to the addition of reheat stages.
(d) Waste heat rejected increases due to the additional heat input required for reheating.
(e) Thermal efficiency slightly decreases due to the lower steam temperature after reheating.
(f) Steam quality at the turbine exit decreases slightly due to the lower steam temperature after reheating.

The Rankine cycle or Rankine Vapor Cycle is the process widely used by power plants such as coal-fired power plants or nuclear reactors. In this mechanism, a fuel is used to produce heat within a boiler, converting water into steam which then expands through a turbine producing useful work.

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Answer:

m g H = 1/2 m v^2     conservation of energy

v = (2 g H)^1/2 = (2 * 9.8 * .2)^1/2 = 1.98 m/s    (call it 2 m/s)

Total momentum of people

N m v = 6E9 * 72 * 2 = 8.6E11 kg m/s       momentum of people

M V = N m v        to get recoil speed of people (conservation momentum)

V = N m v / M = 8.6E11 / 6.0E24 = 1.4E-13

The speed  of the earth would be less than 1/trillionth m/s

The estimated recoil speed of the earth is -1.44 x 10-14 m/s.

First, we need to calculate the total mass of all the people jumping on the earth's surface. This can be done by multiplying the average mass of a person by the total number of people:

Mass of all people = (72 kg)(6 x 109) = 4.32 x 1011 kg

Next, we need to calculate the total momentum of all the people jumping. This can be done by multiplying the total mass of all the people by the distance they jump:

Momentum of all people = (4.32 x 1011 kg)(0.2 m) = 8.64 x 1010 kg m/s

Now, we can use the law of conservation of momentum to find the recoil speed of the earth.

This law states that the total momentum before an event is equal to the total momentum after an event. Therefore, the momentum of the earth before the jump is equal to the negative of the momentum of all the people after the jump:

Momentum of earth = -Momentum of all people = -8.64 x 1010 kg m/s

Finally, we can use the formula for momentum (p = mv) to find the recoil speed of the earth:

v = p/m = (-8.64 x 1010 kg m/s)/(6 x 1024 kg) = -1.44 x 10-14 m/s

Therefore, the estimated recoil speed of the earth is -1.44 x 10-14 m/s.

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1. The horizontal component of the force on the box, given that at force of 18 N was applied at angle of 34° to the horizontal is 15 N

2. The vertical component of the force on the box is 10 N

From the question given above, the following data were obtained:

The horizontal component of the force can be obtained as illustrated below:

Horizontal component of force (Fx) = F × Cosθ

Horizontal component of force (Fx) = 18 × Cos 34

Horizontal component of force (Fx) = 15 N

From the question given above, the following data were obtained:

The vertical component of the force can be obtained as illustrated below

Vertical component of force (Fy) = u × Sine θ

Vertical component of force (Fy) = 18 × Sine 34

Vertical component of force (Fy) = 10 N

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The estimated terminal speed of the wooden sphere falling through air is approximately 8.68 m/s.

To estimate the terminal speed of the wooden sphere falling through air, we can use the following equation:

[tex]V_{terminal}[/tex] = [tex](2mg) / (p_{air} \times Cd \times A \times v^2)[/tex]

Where:

[tex]V_{terminal}[/tex] is the terminal velocity (m/s)

m is the mass of the sphere (kg)

g is the acceleration due to gravity (9.81 m/[tex]s^2[/tex])

[tex]p_{air}[/tex] is the density of air (1.20 kg/[tex]m^3[/tex])

[tex]C_d[/tex] is the drag coefficient (0.500)

A is the cross-sectional area of the sphere ([tex]m^2[/tex])

v is the velocity of the sphere relative to the air (m/s)

First, we need to calculate the mass of the sphere:

[tex]m = (4/3) \times \pi \times r^3 \times p[/tex]

where:

r is the radius of the sphere (m)

ρ is the density of the sphere (kg/[tex]m^3[/tex])

Substituting the given values, we get:

[tex]m = (4/3) \times \pi \times (0.0850 m)^3 \times 830 kg/m^3\\m = 0.980 kg[/tex]

Next, we need to calculate the cross-sectional area of the sphere:

[tex]A = \pi \times r^2\\A = \pi \times (0.0850 m)^2\\A = 0.0228 m^2[/tex]

Now, we can substitute the values into the equation for terminal velocity and solve for [tex]V_{terminal}[/tex] :

[tex]V_{terminal}[/tex] = [tex](2mg) / (p_{air} \times Cd \times A \times v^2)[/tex]

[tex]V_{terminal}[/tex] =[tex](2 \times 0.980 kg \times 9.81 m/s^2) / (1.20 kg/m^3 \times 0.500 \times 0.0228 m^2 \times v^2)[/tex]

[tex]V_{terminal}[/tex] = 8.68 m/s

Therefore, the estimated terminal speed of the wooden sphere falling through air is approximately 8.68 m/s.

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The advantage of having a blowhole on top of a dolphin's head is that it allows them to breathe while swimming without having to break the surface of the water, which is crucial for their survival.

Dolphins are aquatic mammals and need to breathe air to survive. The location of their blowhole on the top of their head allows them to take in air without having to break the surface of the water, which is critical for their survival in the wild. When a dolphin needs to breathe, it can simply surface and quickly exhale and inhale through its blowhole.

This enables them to maintain a constant speed while swimming, and also helps them avoid detection from predators or prey that may be lurking at the surface. In addition, having a blowhole on top of their head allows them to quickly clear their airways of water and mucus, which can be useful for diving and hunting.

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The volumetric strain rate is zero, the vorticity is -1/2μ (∂p/∂x) y, the rate of angular deformation is 1/2μ (∂p/∂x) y, and the shear stress at the plate surface is -1/2 (∂p/∂x) [tex]h^2[/tex].

Given:

x-velocity: u = 1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])

y-velocity: υ = 0 (no variation in y-direction)

where,

μ = dynamic viscosity

p = pressure

x, y = coordinates

h = distance between the plates

To determine the volumetric strain rate, we can start by considering the continuity equation for incompressible flow, which states that the product of velocity and cross-sectional area is constant:

u × (h-y) = Q/A

where A is the cross-sectional area and Q is the volumetric flow rate.

Taking the derivative of both sides with respect to time and simplifying, we get:

dQ/dt = -u × dA/dy

Since the y-velocity is zero, we have dA/dy = 0, so:

dQ/dt = 0

This means that the volumetric flow rate is constant and there is no change in volume with time. Therefore, the volumetric strain rate is zero.

The velocity vector's curl is used to define the vorticity.

ω = ∇ x v

where ∇ is the del operator. For two-dimensional flow, the vorticity is a scalar and can be expressed as:

ω = (∂υ/∂x) - (∂u/∂y)

Substituting the given values for u and υ, we get

ω = 0 - (∂/∂y)[1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])]

Simplifying and integrating with respect to y, we get:

ω = -1/2μ (∂p/∂x) y

The formula for angular deformation rate is:

D = (∂u/∂y + ∂υ/∂x) = ∂u/∂y

Substituting the given value for u, we get:

D = (∂/∂y)[1/2μ (∂p/∂x) [tex](y^2 - h^2)[/tex]]

Simplifying and integrating with respect to y, we get:

D = 1/2μ (∂p/∂x) y

To find the shear stress at the plate surface, we can use the following relation:

τ = μ (∂u/∂y)|y=h

Substituting the given value for u, we get:

τ = μ (∂/∂y)[1/2μ (∂p/∂x) ([tex]y^2 - h^2[/tex])]|y=h

Simplifying, we get:

τ = -1/2 (∂p/∂x) [tex]h^2[/tex]

Therefore, the volumetric strain rate is zero, the vorticity is -1/2μ (∂p/∂x) y, the rate of angular deformation is 1/2μ (∂p/∂x) y, and the shear stress at the plate surface is -1/2 (∂p/∂x) [tex]h^2[/tex].

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Answer:

c

Explanation:

step by step hope this helps you got this!!

In this collision, momentum is conserved as there is no external force acting on the system. We can use the conservation of momentum to find the final velocity of puck 2.

pinitial = m1v1 + m2v2

where m1 and m2 are the masses of puck 1 and puck 2 respectively, and v1 and v2 are their initial velocities. Since puck 2 is initially at rest, we have:

pinitial = m1×v1

Substituting the given values, we get:

pinitial = (0.35 kg)×(2.5 m/s) = 0.875 kg m/s

After the collision, puck 1 is deflected at an angle of 30 degrees with a speed of 1.7 m/s. We can use trigonometry to find the x and y components of its final velocity:

v1x = v1cos(30) = 1.7cos(30) = 1.47 m/s v1y = v1sin(30) = 1.7sin(30) = 0.85 m/s

The final momentum of the system is:

pfinal = m1v1 + m2v2'

where v2' is the final velocity of puck 2. Since momentum is conserved, we have:

pinitial = pfinal

Substituting the given values, we get:

0.875 kg m/s = (0.35 kg)×(1.47 m/s) + (0.51 kg)×v2'

Solving for v2', we get:

v_2' = (0.875 kg m/s - 0.51 kg*(1.47 m/s)) / 0.51 kg = -0.94 m/s

Therefore, the final velocity of puck 2 is -0.94 m/s in the negative x direction (i.e., towards the left).

Consider a collision between two pucks on a frictionless air hockey table. Puck 1 has a mass of 350 g and an initial velocity of 2.5 m/s in the +x direction. Puck 2 has a mass of 510 g and is initially at rest.

After the collision puck 1 has been deflected by 30 degrees and has a speed of 1.7 m/s. What is the speed and direction of puck 2 after the collision?

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To move with the same acceleration as the 10kg box, the 50kg box needs higher net force.

The term "net force" refers to the combined effects of all the forces exerted on a moving body, including gravitational, frictional, and normal forces. FNet equals Fa, Fg, Ff, and FN.

Newton's Second Law of Motion states that

A mass-proportional force is needed to accelerate an item.

The following formula determines the net force necessary to move an item at a given acceleration:

net force = mass x acceleration

The 50kg box and the 10kg box both accelerate at the same rate, but the 50kg box's net force need is more than the 10kg box's because of its heavier mass.

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This lets most of the light through but still blocks some hot air. It will take a long time to pop.

A hypothesis is an educated guess or tentative explanation that serves as a starting point for scientific investigation. It is a statement that suggests a possible relationship between two or more variables that can be tested through research.

A hypothesis should be based on existing knowledge and should be testable through empirical evidence. It should also be falsifiable, meaning that it should be possible to prove it wrong through experimentation or observation. In the scientific method, a hypothesis is usually formulated after conducting a literature review and making observations about the phenomena being studied. Once the hypothesis is established, the researcher can design experiments or collect data to test the hypothesis.

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The oceanic crust is not thicker than the continental crust. The thickness of the continental crust is typically 30 km, compared to the oceanic crust's average thickness of 7 km.

There are two different types of crust that cover the Earth: continental and oceanic. The continental crust is typically up to 25 miles thick, whereas the thinner oceanic crust is typically a little over four miles thick.

The thickness of the continental crust is normally 40 km (25 miles), whereas the thickness of the oceanic crust is only 6 km (4 miles). Different densities of lithospheric rock's impact can be seen in

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The free-body diagram for the crate  shows all the forces acting on the crate like the force applied by the person pushing the crate, the force of friction between the crate and the floor, and the force of gravity acting on the crate.

The free-body diagram for the crate should show all the forces acting on the crate, including the force applied by the person pushing the crate, the force of friction between the crate and the floor, and the force of gravity acting on the crate.

Since the crate is not moving, the force applied by the person pushing the crate must be equal in magnitude and opposite in direction to the force of friction acting on the crate.

This means that the net force on the crate is zero, and the free-body diagram should reflect this.

Here is a description of the forces acting on the crate and a corresponding free-body diagram:

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If the mass of the cylinder is increased, then the temperature of the water will increase because an increase in the mass of the cylinder will result in an increase in the potential energy of the system.

Energy is a fundamental concept in physics that refers to the ability of a system or object to do work. It is a scalar quantity, meaning that it has only magnitude and no direction. Energy can take many forms, including mechanical energy, thermal energy, electrical energy, chemical energy, nuclear energy, and electromagnetic energy. The unit of energy in the International System of Units (SI) is the joule (J), which is defined as the work done by a force of one newton over a distance of one meter (1 J = 1 N × 1 m). Energy can be transferred from one system or object to another, and it can be converted from one form to another. For example, the kinetic energy of a moving object can be converted into thermal energy due to friction, or the chemical energy stored in food can be converted into mechanical energy by the muscles in our bodies. The study of energy and its transformations is a fundamental concept in physics and has important applications in fields such as engineering, environmental science, and renewable energy.

Here,

When the cylinder is heated and placed in the water, its potential energy is converted into thermal energy, which is transferred to the water and causes its temperature to increase. Therefore, an increase in the mass of the cylinder will result in a greater amount of potential energy being converted into thermal energy, leading to a greater increase in the temperature of the water. This hypothesis addresses the lesson question by explaining how an increase in potential energy (due to an increase in the mass of the cylinder) can be converted into thermal energy (due to the heating of the cylinder) in a system.

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The component of the force acting in the direction of an object's motion determines how much force is doing work on that object. The "parallel component" of the force is referred to as this.

A force that is applied perpendicular to an object's motion has no effect since it does not add to the object's kinetic energy.

It follows that the force exerted on the item will increase if the applied force's direction is adjusted to make it more parallel to the direction of motion.

The amount of force accomplishing work will decrease, on the other hand, if the direction of the applied force becomes increasingly perpendicular to the direction of motion.

Take the movement of a box across a rough surface as an illustration.

Only a fraction of the force will be parallel to the surface of the force delivered at a 45-degree angle to the surface, contributing to the motion of the box.

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The labels for vectors A, B, and C ought to be determined by their magnitudes and directions. It is essential to keep track of their angles in relation to the +x axis.

We need to use trigonometry to figure out the y and x-components of each vector in order to find Ay, Ay, B., B, C, and C. The magnitude of the vector is divided by the cosine of its angle with the +x-axis to get the y-component, and the magnitude of the vector is divided by the sine of its angle with the +x-axis to get the x-component.

The Pythagorean theorem can be used to determine the net force. We really want to add the x and y-parts of the vectors to acquire the resultant vector. The Pythagorean theorem can then be used to determine the magnitude of the net force.

In conclusion, we can use the Pythagorean theorem to determine the net force and trigonometry to determine the components of each vector.

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The dog home would measure 5 feet long, 4 feet wide, and 3 feet high (height) or 4 feet (length) x 5 feet (width) x 3 feet (height).

To find the best dimensions for a dog house with a volume of approximately 60 cubic feet, we need to consider several factors such as the size of the dog, the available space for the dog house, and the materials available for construction.

Assuming that the dog is of average size, we can start by considering the shape of the dog house. A rectangular prism is a common shape for a dog house, so we can begin with that shape.

Let's define the dimensions of the dog house as length (L), width (W), and height (H). We can express the volume of the dog house as:

Volume = L x W x H

Given that the volume of the dog house is approximately 60 cubic feet, we can try different combinations of the dimensions to find the best one. One way to do this is to keep one dimension constant and vary the others.

For example, if we keep the length and width constant at 4 feet and 5 feet, respectively, we can find the height by solving the equation:

60 = 4 x 5 x H

H = 3 feet

Therefore, the dimensions of the dog house would be 4 feet (length) x 5 feet (width) x 3 feet (height).

Alternatively, we could keep the length and height constant at 5 feet and 3 feet, respectively, and vary the width:

60 = 5 x W x 3

W = 4 feet

Therefore, the dimensions of the dog house would be 5 feet (length) x 4 feet (width) x 3 feet (height).

Both options result in a volume of approximately 60 cubic feet and provide a comfortable space for the dog. The choice between them would depend on the available space for the dog house and the materials that are available for construction.

Finding the best dimensions for a dog house requires consideration of various factors, such as the size of the dog and the available materials. By experimenting with different combinations of dimensions, we can find the optimal size and shape that provide enough space and comfort for the pet.

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1) The potential energy of the stone when it is at the top of the building is approximately 4313.2 Joules. 2) The height of the hill is approximately 4.09 meter

1.The potential energy of an object at a height h is given by:

PE = mgh

where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s^2 on Earth), and h is the height.

In this case, the mass of the stone is 2.3 kg, the height is 197 m, and g is approximately 9.81 m/s^2. Therefore, the potential energy of the stone when it is at the top of the building is:

PE = mgh = 2.3 kg * 9.81 m/s^2 * 197 m = 4313.2 J

Therefore, the potential energy of the stone when it is at the top of the building is approximately 4313.2 Joules.

2.The total mechanical energy of a ball rolling down a hill is conserved, meaning that the sum of its potential energy and kinetic energy at any point is constant. Therefore, we can use the following formula to solve for the height of the hill:

PE_initial + KE_initial = PE_final + KE_final

where PE is potential energy, KE is kinetic energy, and "initial" and "final" refer to the starting and ending points of the ball's motion.

At the top of the hill, the ball is not moving, so its initial kinetic energy is zero. Therefore, we can simplify the formula to:

PE_initial = PE_final + KE_final

At the bottom of the hill, the ball has a velocity of 9.2 m/s. The final potential energy is zero, since the ball is at the bottom of the hill. Therefore, we can substitute in the known values and solve for the initial potential energy:

PE_initial = PE_final + KE_final

PE_initial = 0 + (1/2) * m * v^2

PE_initial = (1/2) * m * v^2

PE_initial = (1/2) * 0.5 kg * (9.2 m/s)^2

PE_initial = 20.08 J

Now, we can use the formula for potential energy to solve for the height of the hill:

PE_initial = mgh

h = PE_initial / (mg)

h = 20.08 J / (0.5 kg * 9.81 m/s^2)

h = 4.09

Therefore, the height of the hill is approximately 4.09 meter

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Answer:

Explanation:

The object does not carry a charge

The 2m/s is the cat's speed v² when she reaches the tοp οf the incline.

The definitiοn οf velοcity is the rate at which a bοdy mοves in a particular directiοn. Velοcity is the rate at which a distance changes in relatiοn tο time. A vectοr quantity with bοth magnitude and directiοn is velοcity.

The rate οf a directiοnally changing οbject's lοcatiοn. The SI unit οf speed is created by cοmbining the fundamental units οf length and time. Meters per secοnd (m/s) is the unit οf speed in the metric system.

Therefοre, 2m/s is the cat's speed v2 when she reaches the tοp οf the incline.

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The amount of non-conservative work done on the sofa is 3833.83 Joules .

The total work done by the wave is expressed as;

Workdone = Potential energy + Kinetic energy

Workdone = mgh + 1/2mv²

m is the mass = 77kg

g is the acceleration due to gravity = 9.8m/s²

v is the velocity = 8.2m/s

h is the height = 1.65m

Substitute into the formula;

Workdone = 77(9.8) (1.65) + 1/2(77)8.2²

Workdone = 1245.09 + 2588.74

Workdone = 3833.83 Joules

It is a scalar quantity that depends on both the mass and velocity of an object. The formula for calculating kinetic energy is KE = 0.5 * m * v^2, where KE is the kinetic energy, m is the mass of the object, and v is its velocity.

When an object is in motion, it possesses kinetic energy because it has the ability to do work on other objects when it interacts with them. For example, a moving ball has the potential to do work when it collides with another ball, causing it to move and potentially change its direction or speed.

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The Perseid meteors repeat regularly around August 11th or so, despite everything in the solar system moving around, because the debris that creates them follows a consistent orbit.

The orbit of the debris producing the meteor shower is consistent, and it orbits the Sun in the same manner every year. When the Earth crosses through the debris stream, the debris enters the Earth's atmosphere and burns up, producing the Perseid meteor shower.This means that even if the Earth's movement is unpredictable, as it revolves around the Sun, the Perseid meteor shower will occur around the same time every year.

Hence, it's not because of the Earth's movement or other bodies in the solar system that the Perseid meteors repeat regularly around August 11th or so, but because of the consistent orbit of the debris that creates them.

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Translation-Adding more gas to a tank, the internal pressure will increase because by increasing the number of particles?

Adding more gas to a tank, the internal pressure will increase because by increasing the number of particles increases collision between particles.

The frequency of collisions between gas particles and the container walls determines the gas pressure. The number of collisions and consequently the pressure will rise if we fill the container with more gas particles.

The Avogadro Principle (V N) states the frequency of collisions with the container walls must increase as the number of gas particles increases. The pressure of the gas then rises as a result of this. Pressure rises as the number of gas molecules rises while the volume of the container stays the same. Gas pressure rises as container volume decreases. The pressure rises as the temperature of a gas inside a rigid container rises.

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Use a rope or twine to fasten a spring scale to the box. Make sure the rope or string is parallel to the surface and the scale is perpendicular to the surface.

A push force from the outside is applied to a box when it slides, and a frictional force is also applied to the box. The contact sliding motion between the object and the ground causes the frictional force.

Kinetic friction is a kind of sliding friction that occurs often. Kinetic friction is a force that opposes the motion of an object sliding along a surface whenever two objects' surfaces are in contact with one another.

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Answer:

Pool:
1 lap: 100 m distance, 0 m displacement
1.5 laps: 150 m distance, 50 m displacement
2 laps: 200 m distance, 0 m displacement

Track:
1 lap: 200 m distance, 0 m displacement
1.5 laps: 300 m distance, 50 m displacement
2 laps: 400 m distance, 0 m displacement

Explanation:

Distance and displacement are two different things:

Distance is the full length you have traveled. For example, if you swim one lap around a 50 meter pool, you've traveled a distance of 100 meters (there and back).

However, displacement how far you are from the starting point. If you swim one lap around the same pool, your displacement is 0 meters since you ended up in the same place you had started from.

Para encontrar el punto donde están enterradas las llaves del Porsche nuevo, debemos sumar los tres desplazamientos dados en el problema.

Primero, el desplazamiento de A tiene una magnitud de 72.4 m y una dirección de 32.0° al este del norte. Usando trigonometría, podemos descomponer este desplazamiento en sus componentes vertical y horizontal: Componente vertical = 72.4 m sin(32.0°) ≈ 38.9 m hacia el norte. Componente horizontal = 72.4 m cos(32.0°) ≈ 61.5 m hacia el este. Por lo tanto, el desplazamiento de A se puede representar como un vector de 61.5 m hacia el este y 38.9 m hacia el norte. Segundo, el desplazamiento de B tiene una magnitud de 57.3 m y una dirección de 36.0° al sur del oeste. De manera similar, podemos descomponer este desplazamiento en sus componentes vertical y horizontal: Componente vertical = 57.3 m sin(36.0°) ≈ 34.4 m hacia el sur. Componente horizontal = 57.3 m cos(36.0°) ≈ 46.0 m hacia el oeste. Por lo tanto, el desplazamiento de B se puede representar como un vector de 46.0 m hacia el oeste y 34.4 m hacia el sur. Finalmente, el desplazamiento de C tiene una magnitud de 17.8 m hacia el sur. Este desplazamiento solo tiene una componente vertical. Ahora, podemos sumar los tres vectores de desplazamiento para obtener la resultante. Podemos hacer esto sumando las componentes horizontal y vertical por separado: Componente horizontal total = 61.5 m - 46.0 m = 15.5 m hacia el este

Componente vertical total = 38.9 m - 34.4 m - 17.8 m = -13.3 m hacia el norte. La magnitud de la resultante se puede encontrar usando el teorema de Pitágoras: |magnitud resultante| = sqrt((15.5 m)^2 + (-13.3 m)^2) ≈ 20.2 m. Por lo tanto, el concursante ganador debería ir en una dirección de aproximadamente 29.7° al este del norte para encontrar las llaves del Porsche nuevo.

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The acceleration due to gravity at the surface of the planet would be one-twelfth (1/12) of the acceleration due to gravity at the surface of the Earth.

The acceleration due to gravity at the surface of a planet is given by the formula:

g = G * M / R^2

Where:

g is the acceleration due to gravity

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

we are given that the planet has twice the Earth's radius (2R) and one-third of its mass (1/3M).

now, the acceleration due to gravity at the surface of the planet would be:

g = G * (1/3M) / (2R)^2

= G * (1/3M) / 4R^2

= (1/12) * (G * M / R^2)

= (1/12) * gEarth

where gEarth is the acceleration due to gravity at the surface of the Earth.

Hence, the acceleration due to gravity at the surface of the planet would be one-twelfth (1/12) of the acceleration due to gravity at the surface of the Earth.

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Electric potential in y direction (a) will be constant and in x direction (b) will decrease as you move in direction of the electric field.

The electric field E in a region is uniform if it is the same at all points. Specifically, if E has a magnitude of 5 V/m and points in the x direction, then we can say the following about the behavior of the electric potential:

a) In the y direction, the electric potential will be constant. This is because the electric field is perpendicular to the y direction, and therefore does not affect the electric potential in that direction.

b) In the x direction, the electric potential will decrease as you move in the direction of the electric field.

This is because the electric field is parallel to the x direction, and therefore affects the electric potential in that direction. Specifically, the electric potential will decrease by 5 V for every meter you move in the x direction.

To summarize, the electric potential will be constant in the y direction, and will decrease in the x direction as you move in the direction of the electric field. This is due to the fact that the electric field is uniform and points in the x direction.

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A uniform stick has length l, The combined moment of inertia with mass M at one end of the rod is  I₀ + M(L² ÷ 4).

The stick is I₀. The particle is MR² about the point of rotation but R = 1/2 the stick length so for the particle,

I = M × (L ÷ 2)²

I = M × L² × (1 ÷ 2)²

I = (1/4) × M × L²

Therefore, The total I is the sum of the separate is I₀ + (1/4) M L².

Then the combined moment of inertia with mass M at one end of the rod is:

I₀ = (mL²) ÷ 12

I = (mL²) ÷ 12  + M(L ÷ 2)²

I = I₀ + M(L ÷ 2)²

I = I₀ + M(L² ÷ 4)

Therefore, the combined moment of inertia with mass M at one end of the rod is  I₀ + M(L² ÷ 4).

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