Chapter 8, Problem 16P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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 0â€‰m/s , the time for the rider to reach the ground is 0.550â€‰s , the acceleration due to gravity is 9.80â€‰m/s2 , and the final position of the rider is 0â€‰m , maximum height of the bicycle-rider system is 1.48â€‰m , the initial height of the bicycle-rider system is 0â€‰m , the angle of the ramp is 60.0Â° and the time to reach the maximum height is 0.550â€‰s , mass of the bike is 12â€‰kg , the mass of the rider is 72â€‰kg , initial velocity of both bicycle and the rider is 6.22â€‰m/s and the x component of the final velocity of the bike is 21.8â€‰m/s .

Explanation: The conservation of momentum is used to determine the x component of the final velocity of the bicycle as follows (mb+mr)(v0cosÎ¸)=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+v0ytâˆ’12gt2

• 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 0â€‰m for y , 0â€‰m/s for v0y , 0.550â€‰s for t , and 9.80â€‰m/s2 for g to find ymax .

0â€‰m=ymax+(0â€‰m/s)(0.550â€‰s)âˆ’12(9.80â€‰m/s2)(0.550â€‰s)2ymax=1.48â€‰m

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

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

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

ymax=y+v0sinÎ¸tâˆ’12gt2

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

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