A ball is projected vertically up from ground. Boy A standing at the window of first floor of a nearby building observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is `t_(1)`. Another boy B standing on the second floor notices that time interval between the ball passing him twice (during up motion and down motion) is `t_(2)`.
(a) Calculate the height difference (h) between the boy B and A.
(b) Assume that the height of boy A from the point of projection of the ball is also equal to h and calculate the speed with which the ball was projected.

Answer

(a) `h = (g(t_(1)^(2) - t_(2)^(2)))/(8)` (b) `u = (g)/(2) sqrt)2t_(1)^(2) - t_(2)^(2))`