Answer to Question #257190 in Physics for sara

Question

Serving at a speed of 170 km/h, a tennis player hits the ball at a height of 2.5 m and an angle θ below the horizontal. The service line is 11.9 m from the net, which is 0.91 m high. What is the angle θ such that the ball just crosses the net? Will the ball land in the service box, whose out line is 6.40 m from the net?

Answer 1

The horizontal distance to the net: $r=11.9 \text{ m}.$

The horizontal component of velocity:

$$v_x=v\cos\theta,\\\space\\ t=\frac r{v_x}=\frac r{v\cos\theta}.$$

Meanwhile, during the same time t, the ball must cover the height of

$$h=2.5-0.91=1.19\text{ m}.$$

The vertical velocity at the net is

$$u=v\sin\theta+gt.$$

The time is

$$t=\frac{h}{v_\text{avg}}=\frac{2d}{2v\sin\theta+gt},\\\space\\ ht^2+2tv\sin\theta-2h=0,\\\space\\ \frac{hr^2}{v^2\cos^2\theta}+2v\tan\theta-2h=0,\\\space\\ \theta=0.05°.$$