A body is thrown vertically upwards from ground with speed of `10m//s`. If coefficient of restitution of ground, `e=1//2`. Find
(a) the total distance travelled by the time it almost stops.
(b) time elapsed (after the ball has been thrown) when it is at its subsequent maximum height for the third time.

Answer

`(40)/(3)m, (b) t_(e)=3.25s`

Explanation

(a) Total distance `=2h+e^(2)(2h)+e^(4)(2h)+e^(6)(2h)+`--------
`=(2h)/(1-e^(2))=((2)/(1-e^(2)))((v^(2))/(2g))=(v^(2))/(g)((1)/(1-e^(2)))`
`=(100)/(10)((1)/(1-1//4))=(40)/(3)m`
(b) Time `=(2u)/(g)+e((2u)/(g))+e^(2)((u)/(g))=(u)/(g)(2+2e+e^(2))`
`=(10)/(10)(2+1+(1)/(4))=3.25sec`