# Resulting vector angle

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## Main Question or Discussion Point

please help as I'm very old but play Pickleball which is similar to tennis but with a plastic whiffle ball and a solid racket on a reduced size modified tennis court. What I'm trying to figure out is the following: a player on the other side of the net and to the left of me returns the ball that is 135 degrees to where I want to return his shot. The ball is traveling back to me at 1.5 mph. My solid racket will contact the ball returning the ball with a force of 3 mph and facing the the same 135 degrees. Therefore attempting to the ball straight ahead.....However, what angle will the ball leave the racket? I know that the return shot will not be 90 degrees of where the racket is facing.....trying to figure out what the angle the ball leaving the racket will have....many thanks for anyone who can help me....John

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berkeman
Mentor
please help as I'm very old but play Pickleball which is similar to tennis but with a plastic whiffle ball and a solid racket on a reduced size modified tennis court. What I'm trying to figure out is the following: a player on the other side of the net and to the left of me returns the ball that is 135 degrees to where I want to return his shot. The ball is traveling back to me at 1.5 mph. My solid racket will contact the ball returning the ball with a force of 3 mph and facing the the same 135 degrees. Therefore attempting to the ball straight ahead.....However, what angle will the ball leave the racket? I know that the return shot will not be 90 degrees of where the racket is facing.....trying to figure out what the angle the ball leaving the racket will have....many thanks for anyone who can help me....John
A diagram and a video would help a lot. Can you Upload your cellphone video of this shot? Or at least a PDF or JPEG file with a sketch?

To analyze the new trajectory of the ball, the incoming trajectory and the trajectory and angle of the paddle come into play. There are also friction effects between the paddle and ball, but we can deal with that later as a 2nd order effect.

I would love to add a diagram, etc but I am not computer literate enough to do so. Also please disregard the friction right now. What I'm trying to explain is the ball is coming to hit my racket from a 135 degree angle that the racket is facing for a return shot....the ball coming towards the racket is traveling at 1.5 mph and the racket is traveling straight forward parallel to the side line of the court at 3 mph when it hits the ball to return it over the net. What I'm interested in is what angle the ball will leave the racket face as I know the ball won't leave the racket face at 90 degrees to the face of the racket......hope this will clarify my question....thank you....

Correction please use an angle of 50 degrees rather than 135 degrees John

fresh_42
Mentor
Is this the situation?

The angles $a$ are always equally large and this determines where the ball flies to. Of course there are many other factors like what happens during the time the ball is in touch with the racket, friction, spin etc.

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I'm not for sure. Let me further explan. Based on your diagram the 50 degree angle would be from the red line to the face of the racket.....the angle I'm trying to find is the angle between the green line and the face of the racket....

fresh_42
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Well, the formula is $180°=50° + 2\cdot a$ or $a=65°$, so you should be able to calculate any of these angles you like, even if $50°$ might be a different one. The rule is, that the inbound angle $a$ (left) equals the outbound angle $a$ (right). I drew the lines inclined on purpose to emphasize that it has nothing to do with the frame of the picture. You can rotate it as you like.

Thank you for the help....I was under the impression that since the racket was traveling twice as fast as the ball, then when the ball was hit by the racket, the angle in question would be somewhat larger than 50 degrees since the racket speed would influence the angle so that the angle of incidence would not equal the angle of reflection....John

fresh_42
Mentor
Thank you for the help....I was under the impression that since the racket was traveling twice as fast as the ball, then when the ball was hit by the racket, the angle in question would be somewhat larger than 50 degrees since the racket speed would influence the angle so that the angle of incidence would not equal the angle of reflection....John
It can influence it in reality, as it influences the time the ball is in touch with the racket and thus the time you can apply spin, or change direction. However, in the ideal case of zero time on a rigid racket, it is as in the picture. The speed only says how fast it will go, not where. But in reality things are different. E.g. golfers or tennis players always swing the club / racket until the end - through the ball instructors say. This is because the duration of contact is not zero.

Thanks for the answer....That helps...all the best to you and again thank you for the help. John

mfb
Mentor
The two angles are only the same in the frame where the racket is at rest. In this frame the speed doesn't change (assuming the mass of the racket is very large compared to the mass of the ball) or goes down (without that assumption). The diagram of post 5 is impossible.

The reason for my post comes from what I am unable to do n returning the ball. In the example of the ball comining to me at the 50 degree angle from the left over the net to where I want to return the shot, the ball never goes directly at the targeted spot I want he ball returned, but rather to the right of the targeted spot, even though the racket face is directly pointed at the desired targeted spot at impact with the incoming ball...john

mfb
Mentor
This problem is easier to solve experimentally/intuitively than with mathematics. If the ball is coming to the left, you have to point the racket a bit more to the left than the desired target. How much exactly needs practice. You can't hold your racket at a well-calculated angle anyway, and you won't have good velocity data for every shot either.

Thank you mfb, that is the answer that will be helpful to me while playing and confirms my guess as to how to point my racket to prevent the returned ball from going to the right of my targeted area....John

jbriggs444
The angles $a$ are always equally large and this determines where the ball flies to.