You and a friend are sitting on skateboards on the top of a hill. You are behind

Question

You and a friend are sitting on skateboards on the top of a hill. You are behind your friend and hold onto your friend 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 “ 80kg whereas your friend’s mass is mB “ 100kg. (a) How long does it take for the two of you to roll a distance of 50m down the hill (that is along the hypotenuse of the hill, not elevation)? (b) How fast are you traveling when you reach the bottom of the hill?

Explanation / Answer

Angle = arctan 0.20 = 11.31 degree

A) acceleration a = ((m1+m2) g sin theta - u1m1g-u2m2g) /(m1+m2)

= ( 9.8*(80+100)* sin 11.31 degree - 0.2*80*9.8*cos 11.31 degree - 0.15*100*9.8*cos 11.31 degree)) /(100+80)

= 0.2669 m/s^2

Using second equation of motion,

s = 0.5 at^2

t = sqrt (2s/a) = sqrt (2*50/0.2669)

= 19.36 s answer

B) speed at bottom = 0+at = 0.2669*19.36

= 5.17 m/s answer

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