Jack Sock's Serve

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YouTube provides us with an easy way to determine the average velocity of Jack's serve.  The instant Jack contacts the ball is 58.21 seconds into the video.  The ball travels the full length of the 44 foot court, bounces and travels another 4 feet to where Quang hits it at 59.11 seconds.  The elapsed time is 0.87 seconds and the average velocity is 56 ft/sec or 38 mph.  Only 38 mph??  That seems too slow.  Where is the 60 mph serve we've heard about?

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The answer has to do where and how the ball velocity is measured.  The 60 mph serve mentioned at social media sites is measured with a radar gun the instant the ball leaves the paddle.  The average of 38 mph is seemingly low because the ball slows dramatically as it traverses the court.  Using an equation that accounts for aerodynamic drag it is found that the ball velocity as it left Jack's paddle was 52 mph; the average velocity was 38 mph; and the velocity when it reached Quang was about 28 mph.   Jack, most likely could serve the ball at 60 mph or more, but the probability of the serve going long increases to a point where it's not a winning strategy.

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Jack's paddle speed can be estimated using the equation of motion:

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Vrebound = eA * Vinbound + (1+eA) * Vpaddle

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where Vrebound=52

          Vinbound=0

          eA=0.25

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Vpaddle = 41.6 mph