Question

A 0.47 kg banana is thrown directly upward with an initial speed of 4.3 m/s and reaches a maximum height of 0.90 m. What change does air drag cause in the mechanical energy of the banana–Earth system during the ascent?

Answer 1

From the equation of motion,

where final velocity, initial velocity, acceleration, distance traveled.

For the given problem, final velocity is zero since banana reaches maximum height, initial velocity is , acceleration is the acceleration due to gravity. Acceleration due to gravity is taken is negative direction. So equation becomes

To find out the distance traveled without air drag, substitute the values:

The banana travels with air drag.

At the maximum height the total mechanical energy with air drag is equal to potential energy since velocity is zero.

Without air drag the total mechanical energy is

So the change in mechanical energy is

Therefore the mechanical energy of banana-Earth system decreased by