A solid sphere starts from rest at the upper end of the track, as shown in figur

Question

A solid sphere starts from rest at the upper end of the track, as shown in figure below, and rolls without slipping until it rolls off the right-hand end. If H = 13.0 m and h = 1.0 m and the track is horizontal at the right-hand end, how far horizontally from point A does the sphere land on the floor?

https://general.physics.rutgers.edu/gifs/CJ/9-4.gif

A solid sphere starts from rest at the upper end of the track, as shown in figure below, and rolls without slipping until it rolls off the right-hand end. If H = 13.0 m and h = 1.0 m and the track is horizontal at the right-hand end, how far horizontally from point A does the sphere land on the floor? https://general.physics.rutgers.edu/gifs/CJ/9-4.gif

Explanation / Answer

Ignoring air resistance:

At the end of the track, ball has gained energy:
E = 12.0 * 9.81 * m = 117.72 * m (where m = mass of ball)

Horizontal velocity = (E / m)^0.5 = 117.72^0.5 = 10.84m/s

Time for ball to reach floor:
1.0m = 0.5 * 9.81 * t^2
t = 0.2038^0.5
t = 0.4515 seconds

Horizontal distance covered = 10.84 * 0.4515 = 4.89 m

The ball lands 4.89m horizontally from A.

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