Question

a bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike rider is 91kg. What is the kinetic energy of the bike and the rider just before riding up the hill? if the rider just coasts up the hill, at what height will the bike come to a stop?(neglect friction)

Answer 1

Kinetic Energy just before hill:
KE = mv^2 / 2
KE = (91)(8.5)^2 / 2
KE = 3287.4 J

We need to find the point on the hill (height) where the potential energy of being at the location is equal to his current Kinetic Energy. It is at this point that he will no longer have any more KE to help him make it up the rest of the hill.

PE = mgh = KE
h = 3287.4 / mg
h = 3287.4 / (91)(9.8)

h = 3.69 m up the hill