   Chapter 8, Problem 16P

Chapter
Section
Textbook Problem

Spectators watch a bicycle stunt rider travel off the end of a 60.0° ramp, rise to the top of his trajectory and, at that instant, suddenly push his bike away from him so that he falls vertically straight down, reaching the ground 0.550 s later. How far from the rider does the bicycle land if the rider has mass M = 72.0 kg and the bike has mass m = 12.0 kg? Neglect air resistance and assume the ground is level.

To determine
The distance of the bicycle from the rider.

Explanation

Given Info: The initial downward velocity of the rider is 0m/s , the time for the rider to reach the ground is 0.550s , the acceleration due to gravity is 9.80m/s2 , and the final position of the rider is 0m , maximum height of the bicycle-rider system is 1.48m , the initial height of the bicycle-rider system is 0m , the angle of the ramp is 60.0° and the time to reach the maximum height is 0.550s , mass of the bike is 12kg , the mass of the rider is 72kg , initial velocity of both bicycle and the rider is 6.22m/s and the x component of the final velocity of the bike is 21.8m/s .

Explanation: The conservation of momentum is used to determine the x component of the final velocity of the bicycle as follows (mb+mr)(v0cosθ)=mbvb,f+mrvr,f and this expression is rearranged to the final velocity of the bicycle.

The formula for the maximum height of the bicycle-rider system is,

y=ymax+v0yt12gt2

• ymax is the maximum height reached by the bicycle-rider system.
• v0y is the initial downward velocity of the rider.
• t is the time for the rider to reach the ground.
• g s acceleration due to gravity.

Substitute 0m for y , 0m/s for v0y , 0.550s for t , and 9.80m/s2 for g to find ymax .

0m=ymax+(0m/s)(0.550s)12(9.80m/s2)(0.550s)2ymax=1.48m

Thus, the maximum height reached by the bicycle-rider system is 1.48m .

Given info: The maximum height of the bicycle-rider system is 1.48m , the initial height of the bicycle-rider system is 0m , the angle of the ramp is 60.0° , the time to reach the maximum height is 0.550s , and the acceleration due to gravity is 9.80m/s2 .

The formula for the initial velocity of the bicycle-rider system is,

ymax=y+v0sinθt12gt2

• ymax is the maximum height reached by the bicycle-rider system.
• v0 is the initial velocity of bicycle-rider system

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