A tennis ball is struck at the base line of the court, 13.0 m from the net. The ball is given an initial velocity with a horizontal component equal to 26.0 m/s at an initial elevation of 1.50 m.

Question

(a) What vertical component of initial velocity must be given to the ball, such that it barely clears the 1.00 m high net?

(b) How far beyond the net will the ball hit the ground?

Answer 1

a) This is an asymmetric launching problem, so the full equations of motion must be used:

y = y₀ + v_y0t - 1/2 gt² and x = x₀ + v_x0t

You can use the 2nd equation to solve for the time to the net: t_net = 13m/16m/s

Now you can solve for v_y0 in the 1st equation with y = 1, t=t_net, y₀= 1.5, and g = 9.8

b) You can solve the 1st equation for time in the air (it will be a quadratic (you have to use quadratic formula) with y = 0

Once you have t_air x = v_x0t_air and the distance behind the net will be x -13.