Question

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 show that the speed of the banana just before hitting the water is v

Answer 1

The mass of the banana is m and it is at height h.

Applying the Law of Conservation of Energy

Total Energy before fall = Total Energy after fall

`E_(i)` =
`E_(f)`

Here, total energy is the sum of kinetic energy and potential energy

`K.E_(i)` +
`P.E_(i)` =
`K.E_(f)` +
`P.E_(f)` (a)

When banana is at height h, it has

`K.E_(i)` = 0 and
`P.E_(i)` = mgh

and when it reaches the river, it has

`K.E_(f)` = 1/2m
`v^(2)` and
`P.E_(f)` = 0

Putting the values in equation (a)

0 + mgh = 1/2m
`v^(2)` + 0

mgh = 1/2m
`v^(2)`

cutting 'm' from both sides

gh = 1/2
`v^(2)`

v =
`√(2gh)`

Hence, the velocity of banana before hitting the water is

v =
`√(2gh)`