Question

A tennis player wants to slam a serve at O at height h above the court so that the ball lands just inside the opposite corner of the court. The court has length L and width W. What should the ratio be, where vov is the vertical component and voH the horizontal component of the initial velocity Vo? The time racket. 0 is the time when the ball is hit by the IV

Answer 1

1. 
   According to the question, the is to be done at point O. at a height 'h' from the ground. at time t = 0 is the time when the ball is hit by the racket with initial velocity nu_0. So, at t = 0, the co-ordinate of the ball, (H, V,) identicalto (0, h) identicalto = (x_0, y_0). H = horizontal co-ordinate = y_0 v = vertical co-ordinate = x_0 let, after time t the ball hit the ground. and the final co-ordinate of the ball is, (x', y') identicalto (x', 0) now, we consider the the y-axis to be along. the height h, i. e upwards. now, to the ball so that it touches ground. the ball is to be pushed down wards. and the gravitational acceleration also acts downwards i. e along -ve y axis. now, y' = y_0 - v_0y t - 1/2 gt^2 rightdoublearrow 0 = h - v_0y t - 1/2 gt^2 rightdoublearrow v_0y middot t = h - 1/2 gt^2 (1)
   
2.