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

$170\ (km/h)=47.22\ (m/s)$

$v_{0x}=47.22\cdot\cos\theta$

$11.9=v_{0x}\cdot t_1=47.22\cdot\cos\theta\cdot t_1$

$2.5-0.91=47.22\cdot\sin \theta\cdot t_1+gt_1^2/2$ . From these two equations

$0.311\tan^2\theta+11.9\tan\theta-1.279=0\to \theta=6.1°$ . Answer

Time of movement in the vertical direction

$2.5=47.22\cdot\sin6.1°\cdot t_2+9.8\cdot t_2^2/2\to t_2=0.367\ (s)$

$l=47.22\cdot\cos6.1°\cdot0.367=17.2\ (m)$

The service box is placed at a distance $11.9+6.4=18.3\ (m)$ . So,

the ball will not land in the service box. Answer