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Chapter Question #65 — I think the x-components of the ball bouncing off of the wall would be equal and opposite to one another with a sum = 0. The y-components, opposite the 36-degree angle would be equal to 5.51(sin 36). This quantity would be doubled. I calculate that the change in momentum would be 6.5 kg*m/s. Am I going wrong somewhere?
A little bit! Remember, momentum has direction. So in the x direction, lets call the initial momentum positive. Then the final momentum would be negative. Impulse is change in momentum, so it is final (negative) minus initial (positive). Since both are equal, we do get twice 38 cos 36 degrees. That makes sense because the normal is perpendicular to the wall, so the only force exerted on the ball is in the x direction. There is zero change in momentum in the y direction since initial and final momenta are in the same direction. Having said all this, the answer key is still wrong and it even has the wrong units. I will upload a corrected version shortly. Thanks for the comment! John
Got it — Thanks John!!
I am having a problem with #40 (baseball reaching batter at 32 m/s). I can't seem to get 114 m/s for the speed of the outgoing ball. How should I approach this problem.
Manuel, the key to the problem is that it is an elastic collision. Use the relative velocity formula for elastic collisions: (v sub 1 minus v sub 2) = -(v prime sub 1 minus v prime sub 2). v prime is the velocity of the objects after the collision. Have the baseball initially moving in the positive x direction. The bat is moving in the neg x direction with the same speed both before and after the collision. If that doesn't help, please let me know and I'll post the solution. John
Got it. Thank you very much John.