Charles Finley
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Hey all, so I've got a math project due this weekend and I could seriously use some advice. I am trying to figure out a way to calculate tennis serve speed given a video. I am using this 6000 FPS video here:
Assuming the racket string tension to be 50 lbs (222.41N) I used vectors and geometry to calculate the force exerted on the ball based on the angle from the top of the racket to the ball as it bent the strings. I did this for each frame and then created a Force vs. Time graph. The strongest force I found exerted on the ball was 93N (when the ball was furthest back in the strings, shown in the picture I attached) and the weakest force 11N, the frame right before the ball leaves the strings (again, if this doesn't make sense or work let me know).
On my F/T graph I used frame count (so 1-16) on the x-axis and force (N) on the y-axis. I found the integral to be 839. But I thought that using the frame count on my x-axis might be flawed so I converted to seconds and got the integral (impulse) to be approximately .16. I divided this by the mass (kg) of the tennis ball and got 2.759 m/s, or about 6 miles per hour, which I am assuming would be the final velocity.
Unfortunately, I know the speed of the serve to be 142 mph and thus this does not make any sense. If anyone sees where I went wrong or knows a better way to go about this, any help is appreciated. I attached an image of how I found the force in each frame in case anyone wants too see that.
Assuming the racket string tension to be 50 lbs (222.41N) I used vectors and geometry to calculate the force exerted on the ball based on the angle from the top of the racket to the ball as it bent the strings. I did this for each frame and then created a Force vs. Time graph. The strongest force I found exerted on the ball was 93N (when the ball was furthest back in the strings, shown in the picture I attached) and the weakest force 11N, the frame right before the ball leaves the strings (again, if this doesn't make sense or work let me know).
On my F/T graph I used frame count (so 1-16) on the x-axis and force (N) on the y-axis. I found the integral to be 839. But I thought that using the frame count on my x-axis might be flawed so I converted to seconds and got the integral (impulse) to be approximately .16. I divided this by the mass (kg) of the tennis ball and got 2.759 m/s, or about 6 miles per hour, which I am assuming would be the final velocity.
Unfortunately, I know the speed of the serve to be 142 mph and thus this does not make any sense. If anyone sees where I went wrong or knows a better way to go about this, any help is appreciated. I attached an image of how I found the force in each frame in case anyone wants too see that.
