Calculating a Tennis Player's Ball Speed

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Homework Help Overview

The problem involves calculating the initial speed of a tennis ball hit by a player standing 12.3 m from the net, with the ball needing to rise at least 0.33 m to clear the net. The player hits the ball at an angle of 3° above the horizontal.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the vertical and overall speed of the ball, with one participant attempting to calculate the initial vertical velocity and questioning if trigonometric functions can be used to find the horizontal component of the speed.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and clarifying the distinction between vertical velocity and overall speed. Some guidance has been provided regarding the relationship between the components of the ball's velocity.

Contextual Notes

There is a focus on the angle of projection and the need to consider both vertical and horizontal components of the ball's speed. The original poster's calculations and assumptions are being scrutinized for accuracy.

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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