A ball rolls without slipping down the track as shown in the figure below, start

Question

A ball rolls without slipping down the track as shown in the figure below, starting from rest at a height h1 = 25 m as shown. The ball is traveling horizontally when it leaves the bottom of the track, which has a height h2 = 9.1m. Find where the ball hits the ground; that is, find L.
L =__________m

A ball rolls without slipping down the track as shown in the figure below, starting from rest at a height h1 = 25 m as shown. The ball is traveling horizontally when it leaves the bottom of the track, which has a height h2 = 9.1m. Find where the ball hits the ground; that is, find L.

Explanation / Answer

m g (h1 - h2) = 0.5 m v^2 + 0.5 I w^2

m g (h1 - h2) = 0.5 m v^2 + 0.5 (2/5 m R^2) (v/R)^2

g (h1 - h2) = 0.5 v^2 + (1/5) v^2

v = sqrt(9.8*(25-9.1)/0.7)

v = 14.9198 m/s

-9.1 = -0.5*9.8*t^2 ==> t = 1.36277 s

L = v t = 14.9198 * 1.36277 = 20.33 m

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