Question

A ball is dropped from height h on the ground level. If the coefficient of restitution is e then the height upto which the ball will go after \(\sf n^{th}\) jump will be

Answer 1

@IrishBoy123

Answer 2

@radar

Answer 3

@iambatman

Answer 4

\[v= \sqrt{2gh}\]
\[e = \frac{ v' }{ v _{0} } = \sqrt{\frac{ H }{ h }}\]
thus
\[H = e ^{2}*h\]
let's us now use the new height to make the same calculation
\[H _{1}= e ^{2}*H = e ^{2}*e ^{2}*h = e ^{4}*h\]
that is enough to get the pattern
\[H _{n} = e ^{2*n} * h\]

Answer 5

Thanks @catch.me

Answer 6

you are welcome :)