Question

In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H = 5.5 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor?

Answer 1

using conservation of energy

mgH = 1/2mv² + 1/2Iw² + mgh

where ,

I = 2/5 * m * r²

and

w = v/r

we have

mgH = 1/2mv² + 1/2 * 2/5 * m * r² * v² / r² + mgh

gH = 7/10 v² + gh

v = sqrt ( 10 g (H -h) / 7 )

v = sqrt ( 10 ( 5.5 - 2) / 7)

v = 7 m/s

so,

now, we can find time in air

t = sqrt ( 2h / g)

t = sqrt ( 2 * 2 / 9.8)

t = 0.6388 sec

so,

horizontal distance

d = vt

d = 4.472 m