A ball is dropped on a large smooth inclined plane of angle of inclination `37^(@)`, from a height of `(20)/(9)m` above the point of impact. The coefficient of restitution of the impact is `e = (9)/(16)` then :
[Take `g = 10 m//s^(2)`]

Options

A. The velocity of the ball just after the first impact is 5 m/s
B. The maximum distance between the incline and the ball between the first and second impact is `(9)/(16) m`
C. The time interval between the first and second impact between the ball and incline plane is `(3)/(4) s`
D. The time interval between the first and second impact between the ball incline plane is 2s.

Answer

A, B, C

Explanation

`V^(2)=2gh = 2xx10xx(20)/(g)rArr V=(20)/(3)m//s`
`V_(x)=V sin 37^(@) = 4m//sV_(y) = eV cos 37^(@) = 3m//s`
`:. V` makes an angle of `37^(@)` with incline plane
`T=(2V'sin 37^(@))/(g cos 37^(@))=(3)/(4)s`
is the time of flight on incline plane
`H=(V'^(2)sin^(2)37^(@))/(2g cos 37^(@)) = (9)/(16) m`.