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Two billiard balls, each of mass 30 g, hit a rigid wall with the same speed of 108 km/h but at different angles, and each rebounds with the same speed it arrived with. If both balls strike the wall at 30 deg to the wall's surface (ball 'a' approaching from one side and ball 'b' from the other), what is the ratio of the magnitudes of the impulses given to ball 'a' and ball 'b' by the wall measured along the X-direction (normal to the wall)?
- 1: 1
- sqrt(2): 1
- 2: 1
- 1: sqrt(2)
Correct answer: 1: 1
Solution
Each ball reverses only its normal (X) velocity component, so the X-impulse magnitude is 2*m*v*cos(theta). Since both balls have equal mass, equal speed, and the same incidence geometry, their X-impulses are equal, giving a ratio of 1: 1.
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