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Answer to Question #5395 in Mechanics | Relativity for Marissa
Question #5395
a ball of mass m traveling horizontally with velocity v strikes a wall and rebounds back along its original path with no change in its speed what is the magniture of thee impulse delivered to the ball by the wall
Expert's answer
The impulse before the collision the ball:
<img style="width: 69px; height: 39px;" src="data:image/png;base64,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" alt="">
The impulse after the collision the ball:
<img style="width: 74px; height: 36px;" src="data:image/png;base64,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" alt="">
The impulse delivered to the ball by the wall:
<img style="width: 168px; height: 34px;" src="data:image/png;base64,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" alt="">
Hence
<img style="width: 81px; height: 27px;" src="data:image/png;base64,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" alt="">
<img style="width: 69px; height: 39px;" src="data:image/png;base64,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" alt="">
The impulse after the collision the ball:
<img style="width: 74px; height: 36px;" src="data:image/png;base64,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" alt="">
The impulse delivered to the ball by the wall:
<img style="width: 168px; height: 34px;" src="data:image/png;base64,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" alt="">
Hence
<img style="width: 81px; height: 27px;" src="data:image/png;base64,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" alt="">
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