A toy hovercraft is given a quick shove atthe bottom of a ramp. The ramp makes a

Question

A toy hovercraft is given a quick shove atthe bottom of a ramp. The ramp makes an angle of 30° with the horizontal. There is no friction between the hovercraft and the ramp. The hovercraft has a mass of 0.4 kg. At the instant shown, the hovercraft is at point A and has a speed of 2 m/s. The hovercraft travels up the ramp, comes to rest at point B, and then travels   down the ramp

What is the kinetic energy of the hovercraft at point A? Show your work, and express your answer in Joules.

What is the potential energy of the hovercraft at point B? Explain how you can tell.

How high above point A is point B? (Give the vertical distance, not the distance along the ramp.) Show how you obtained your answer.

What is the speed of the hovercraft when it reaches point A again? Explain your reasoning.

Explanation / Answer

The kinetic energy at point A is

K=0.5mv^2=0.5(0.4)(2)^2=0.8 J

The potential energy at B is 0.8 J

the height is h=0.8/0.4*9.8*tan30=0.35 m

Conservation of energy at any point is conserved.
         ThereforeKepointA + UpointA = KepointB +UpointB

If you take point A, the lower point, to have potential energy (U)to equal zero. (you have the right to take the origin at anypoint). Therefore, at point A, you have solely Kinetic Energy (Ke).Also, at point B, the higher point, Kinetic energy is zero (as itis stated Velocity goes to zero at point B). Therefore, at point Bit is solely potential energy.
         ThereforeKepointA = UpointB
               Since KepointA was found, you can solve forUpointB

**It is important to note that the velocity is parallel to theplane, but the height is in the Y direction, so you'll have to usetrigonometry identies (sin, cos, or tan) to solve the change in y,and therefore the height**

Now that you know potential energy, you can use U = mgh where h isthe change of height from point A to point B.

Finally, if you know potential energy at point B, you can solve forKe at point A, and therefore the velocity. However, common sensewould tell you that if there are no external forces or frictionpresent the velocity at point A should be the same at bothtimes.

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