A ball is projected from the ground at some angle with horizontal. Coefficient of restitution between the ball and the ground is e. Let a, b and c be the ratio of times of flight, horizontal range and maximum height in two successive paths. Find a, b and c in terms of e.

Answer

A, B

Explanation

Just after collision x-component of velocity remain unchanged but y-component of velocity become `e` times.

Now, `T=(2u_y)/(g)`, `H=(u_y^2)/(2g)` and `R=(2u_xu_y)/(g)`
or `Tpropu_y`, `Hpropu_y^2` and `Rpropu_y`
`:. T_1/T_2=a=(u_y)/(eu_y)=1/e`
`R_1/R_2=b=(u_y)/(eu_y)=1/e`
and `H_1/H_2=c=((u_y)^2)/((eu_y)^2)=1/e^2`