1-D motion Incline question.

Question

A person riding a bike has traveled 76.3 m up a hill inclined at 16.0°. At that point, the chain on the bike breaks, so the rider stops and coasts back down the hill. How much time does it take to make it back to the bottom of the hill?

Answer 1

1. At the 76.3m point, the speed of the bike is zero, while the acceleration of the bike along the incline is g*sin(theta), where theta is 16
2. So the time it takes to travel the 76.3m done the hill is given by

S = 1/2 a t² = 1/2 g sin(16) t² = 76.3

t = sqrt(2 * 76.3/(9.8 *sin(16))) = 7.5 s