physics word problem

Question

A small catapult is used to launch 1.5 kg water balloons straight up into the air. A clever student is able to measure the speed of the water balloon while it is rising up into the air. She finds that the water balloon is 8.0 m above the catapult it is moving at a speed of 20.0 m/s. (For the purposes of this question, assume that the catapult is positioned in a small hole so that the height of the catapult is level with the ground.)

c) With what speed with the water balloon hit the ground?

d) If the catapult was 75% efficient, how much energy was stored in the catapult before the water balloon what launched?

e) What happened to the 25% of the energy that was not transferred to the water balloon?

Answer 1

Hi Stephen,

This problem is asking you to work with the conservation of energy.

At the instant the water balloon is launched, all of its energy is in the form of kinetic energy and has no potential energy, as it is at ground level. In numbers, PE = 0, and KE = 1/2 mv^2, where v is its starting velocity. We are also given its velocity at a later time. Now PE is not zero, it is mgh, mass times the acceleration due to gravity times height. Because we are given both height and velocity, we can calculate its total energy at this point. This total energy must be constant throughout the flight of the balloon, so it must be the same as the total energy when it started and when it hits the ground. Since when the balloon hits the ground its PE = 0 again, we can solve for v, since its final KE + PE must equal its total energy at the point given in the problem.

All of the balloon's energy comes from the catapult. We can calculate the total energy of the balloon by doing PE + KE at the point given in the problem. Since the catapult is only 75% efficient, the total energy of the catapult must satisfy 0.75 * catapult energy = balloon energy.

Where did this extra energy go? Some of the stored potential energy of the catapult will be dissipated as heat or sound when the mechanism is activated. This could be due to friction, for example. What's important to note is that no energy is actually lost, it just did not end up in the balloon.

Please feel free to message me if you have more questions.

-Cole