A bicyclist starting from rest applies a force of F = 324 N to ride his bicycle

Question

A bicyclist starting from rest applies a force of F = 324 N to ride his bicycle across flat ground for a distance of d = 305 m before encountering a hill making an angle of theta = 21 degrees with respect to the horizontal The bicycle and rider have a mass of m = 146 kg combined. (a) How much work, W in joules, did the rider do before reaching the hill? deduction per feedback (b) What it the bicycle's speed v in m/s, just before the hill? Assume there is no kinetic friction between the bicycle and the ground. (c) If the cyclist starts coasting at the bottom of the kill, what distance, d in meters, does the bike travel up the incline?

Explanation / Answer

1. Work = F * d
= 324 * 305
= 98.82 kJ

2.Ek = 1/2 m v^2
v^2 = 2Ek / m
v = sqrt( 2 Ek/m) = 36.79 m/s

3.

Ek = mgh
= mg * d sin( theta)
d = Ek / ( mg sin(theta) )

98.82e3/(146*9.8sin21)= 192.724 m

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