Question

A bicyclist is traveling at a speed of 20.0 m/s as he approaches the bottom of a hill. He decides to coast up the hill and stops upon reaching the top. Determine the vertical height of the hill. Ignore friction and air resistance.A) 28.5 m B) 3.70 m C) 11.2 m D) 40.8 m E) 20.4 m

Answer 1

Answer:

Vertical height of the hill, h = 20.4 meters

Explanation:

Given that,

Speed of the bicyclist, v = 20 m/s

To find,

The vertical height of the hill.

Solution,

Let h is the height of the hill. When he approaches the bottom of the hill, the loss in kinetic energy is equal to the gain in potential energy. Using the conservation of energy as,

$\dfrac{1}{2}mv^2=mgh$

$h=\dfrac{v^2}{2g}$

$h=\dfrac{(20)^2}{2\times 9.8}$

h = 20.4 meters

Therefore, the vertical height of the hill is 20.4 meters. Hence, this is the required solution.