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# Mechanics 3, Sphere impact with a fixed surface question watch

1. Question: The coefficient of restitution between a smooth ball and a plane surface is e. The ball strikes the surface at an angle theta and rebounds at right angles to its original direction of motion. Express theta in terms of e.

My working:
-e(vsin(theta))=vsin(90-theta)
-e(vsin(theta))=vcos(theta)
-e=cot(theta)
theta=cot^-1(-e)

My problem is that the textbook answer is cot^-1 (sqroot e)

Anyone know where I went wrong? I have no idea where the sqroot comes from...
2. (Original post by nair39)
Question: The coefficient of restitution between a smooth ball and a plane surface is e. The ball strikes the surface at an angle theta and rebounds at right angles to its original direction of motion. Express theta in terms of e.

My working:
-e(vsin(theta))=vsin(90-theta)
-e(vsin(theta))=vcos(theta)
-e=cot(theta)
theta=cot^-1(-e)

My problem is that the textbook answer is cot^-1 (sqroot e)

Anyone know where I went wrong? I have no idea where the sqroot comes from...
You have assumed that the speed remains constant but it does not.
Use a different letter for the velocity after the impact and use the facy that there is no change in momentum parallel to the surface.
3. (Original post by brianeverit)
You have assumed that the speed remains constant but it does not.
Use a different letter for the velocity after the impact and use the facy that there is no change in momentum parallel to the surface.
Oh right I see, I shouldn't have made that assumption. I made the same assumption in a previous question and I got it right, but I guess that was a slightly different situation. Thanks a lot.

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