Calculating a Tennis Player's Ball Speed

AI Thread Summary
To determine the initial speed of a tennis ball hit at a 3° angle to clear a net 0.33m high from a distance of 12.3m, the vertical component of the speed was calculated as 2.54 m/s. However, this only represents the vertical velocity, not the overall initial velocity. The relationship between the vertical and horizontal components suggests that the total speed is greater, and using trigonometry, the correct calculation yields an initial speed of approximately 48.5 m/s. This highlights the importance of considering both vertical and horizontal components in projectile motion. The discussion confirms that the initial speed of the ball is significantly higher than initially calculated.
bd24
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Homework Statement


a tennis player standing 12.3 m from the net hits the ball at 3° above the horizontal. to clear the net the ball must rise at least 0.33m. if the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

my answer was found by the equation u^2/2g = d (0.33m)
so 0.33m x 19.6 ms^2 = 6.47 ms
the square root of 6.47 ms
= 2.54 ms

Is this right?
 
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Hi bd24

You found the initial vertical velocity, not the initial velocity (which I think the question is asking)
 
The ball does have to move at that speed upwards, but the ball left the racket 3 degrees above the horizontal. The speed of the ball was a lot faster than 2.54 ms. How is speed in the Y direction related to the overall speed.
 
hmmm, so now i have the speed of the ball in the vertical, is it possible to use trig to solve for the horizontal speed? like 2.54/sin(3°) = 48.5 ms?
ps. thanks for all the help
 
Yes, that's the answer
 

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