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A hard-thrown football has a mass of 0.410 kg and a speed of 25.0 m/s, while the 110 kg player throwing it runs at 8.00 m/s. Roughly how many times greater is the player's momentum than the ball's momentum?
AAbout 860 times
BAbout 8.6 times
CAbout 86 times
DAbout 4.3 times
Answer & Solution
Correct answer: C. About 86 times
1. The player's momentum is (110 kg)(8.00 m/s), which is 880 kg m/s.
2. The ball's momentum is (0.410 kg)(25.0 m/s), which is 10.3 kg m/s.
3. Dividing the player's momentum by the ball's momentum gives 880 divided by 10.3, which is about 86.
4. Even though the ball moves faster, the player's much larger mass gives him far greater momentum overall.
5. 8.6 times and 860 times are both off from the correct ratio by a factor of ten in opposite directions.
_Source: OpenStax College Physics (CC BY 4.0), Ch 8 "Linear Momentum and Collisions", section 8.1 Linear Momentum and Force_
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