Emily holds a banana of mass m over the edge of a bridge of height h. She drops the banana and it falls to the river below. Use conservation of energy to find the speed of the banana just before hitting the water. Express your answer in terms of some or all of the variables h and m, and appropriate constants.

The speed of the banana just before it hits the water is:

√ (2 · g · h) = v

Explanation:

Hi there!

Before Emily throws the banana, its potential energy is:

PE = m · g · h

Where:

PE = potential energy.

m = mass of the banana.

g = acceleration of the banana due to gravity.

h = height of the bridge (distance from the bridge to the ground).

When the banana reaches the water, all its potential energy will have converted to kinetic energy. The equation for kinetic energy is as follows:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass of the banana.

v = speed.

Then, when the banana hits the water:

m · g · h = 1/2 · m · v²

multiply by 2 and divide by m both sides of the equation:

2 · g · h = v²

√ (2 · g · h) = v