Question

A bike coasts up a long hill. The hill has an incline of 38 degrees. The mass of the bike and rider is 129kg. If the bike starts up the hill at a velocity of 10 m/s, how far will the rider go up the hill before stopping? The coefficient of kinetic friction is .30 .

Answer 1

Answer on question #56694, Physics / Other

Question A bike coasts up a long hill. The hill has an incline of 38 degrees. The mass of the bike and rider is 129kg. If the bike starts up the hill at a velocity of 10 m/s, how far will the rider go up the hill before stopping? The coefficient of kinetic friction is .30 .

Solution Let us find deceleration

$a=\frac{F}{m}$ $=\frac{mg\sin\alpha+\mu mg\cos\alpha}{m}=g(\sin\alpha+\mu\cos\alpha)=$

$=9.8(\sin 38{}^{\circ}+0.3\cos 38{}^{\circ})=8.36\,m/s^{2}$

Now lets find time of riding:

$t=\frac{v}{a}=\frac{10}{8.36}\approx 1.2\,s$

Now we can find how far will the rider go up the hill before stopping

$s=v_{0}t-at^{2}/2=10\cdot 1.2-8.36\cdot 1.2^{2}/2\approx 6\,m$