If a ball is thrown from the ground with velocity \(u \, m/s\) upwards in a gravitation field with \(g \,m/s^2\)

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B

C

D

E

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If a ball is thrown from the ground with velocity \(u \, m/s\) upwards in a gravitation field with \(g \,m/s^2\) acceleration working downwards. The ball is rebounded and for each rebound, the velocity reduces to f times of previous velocity (\(0<f<1\)). What is the total distance travelled by the ball since the time it is thrown upwards for the first time?

A. \(\dfrac{u^2}{g\left(1-f^2\right)}\)

B. \(\dfrac{u^2}{g\left(1-f\right)}\)

C. \(\dfrac{u}{g\left(1-f^2\right)}\)

D. \(\dfrac{u^2}{gf^2}\)

E. \(\dfrac{u}{gf^2}\)

The OA is A