(1) You and a friend are sitting on skateboards on the top of a hill. You are in

Question

(1) You and a friend are sitting on skateboards on the top of a hill. You are in front of your friend and your friend holds onto you from behind. The hill has a 20% grade to it. The coefficient of rolling friction for you is µr “ 0.2 and the coefficient of rolling friction for your friend is µr “ 0.15. You have a mass of mA “ 80 kg whereas your friend’s mass is mB “ 100 kg. (a) How long does it take for the two of you to roll 50 m down the hill? (b) How fast are you traveling when you reach the bottom of the hill?

Explanation / Answer

given,

grade = 20 % so,

angle = tan^-1(20 / 100)

angle = 11.31 degree

mA = 80 kg

force equation of mA will be

mg * sin(11.31) - k * mg * cos(11.31) = ma

9.8 * sin(11.31) - 0.2 * 9.8 * cos(11.31) = a

a = 0.0000117785 m/s^2

s = at^2

50 = 0.0000117785 * t^2

t = 2060.35 sec

it'll take 2060.35 sec to roll 50 m down the hill

v^2 = u^2 + 2as

v^2 = 0 + 2 * 0.0000117785 * 50

v = 0.03431 m/s

velocity on reaching the bottom = 0.03431 m/s

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