Question

During the semi-finals of the U. S. Open 2007 Grand Slam Tennis, Venus Williams was in the second set of her match against Justine Henin when her serve was clocked (by a radar gun) at 77 miles per hour. The ball left her racquet horizontally at a height of 2.37 m above the surface of the tennis court. Venus was standing at the service line 12.0 m from the net that has a height of 0.9 m. If the ball clears the net and lands within 7.0 m of the net on the other side, the serve is considered “good" according to the regulations of the game because the ball lands inside the service box on the other side of the net. (See the sketch of a tennis court below.) If the ball clears the net but lands beyond the service box on the other side, this serve is considered a fault. The player receiving the service ball cannot hit the ball before it strikes the court inside the service box. (a) With what minimum speed (in SI units) is Venus required to strike the ball for it to just clear the net? State assumption(s) and support your response quantitatively. (b) Was the serve clocked at 77 miles per hour "good" or was it a fault? If this ball goes over the net, how far will it land from the backline of the service box on Justine’s side of the net. Support your response quantitatively. (c) Sketch graphs of the ball’s displacement, velocity, and acceleration as functions of time (six graphs.) (d) Williams’ slowest serve was at 71 miles per hour. She used the same technique described above but she obviously did not strike this ball as hard. After the match, a local sportscaster said "By serving a slower ball that cleared the net, Williams gave Henin more time to react to her serve because the ball was in the air a little longer than when Williams served her fast ball". Does the sportscaster speak with authority on this subject? Use physics principles to support your response.