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I'm playing a game of pool with by brother; he's stripes. At some point, I notice I have a perfectly-aligned shot to put the 1-ball in the corner pocket. But I have to be careful; if I hit the cue too hard, I'll pocket my brother's ball as well. If my shot angle = 27°, and I've estimated the dimensions at the bottom (figure not to scale) in inches, how much initial velocity do I need to give the cue ball in order to pocket my ball but not my brother's? Reminder: the mass of a standard pool ball is 6 oz, the diameter is 2.25 inches, the coefficient of restitution for pool ball impacts is approximately 0.95, and the coefficient of rolling friction between a pool ball and the cloth is μ, ≈ 0.01.

I'm playing a game of pool with by brother; he's stripes. At some point, I notice I have a perfectly-aligned shot to put the 1-ball in the corner pocket. But I have to be careful; if I hit the cue too hard, I'll pocket my brother's ball as well. If my shot angle = 27°, and I've estimated the dimensions at the bottom (figure not to scale) in inches, how much initial velocity do I need to give the cue ball in order to pocket my ball but not my brother's? Reminder: the mass of a standard pool ball is 6 oz, the diameter is 2.25 inches, the coefficient of restitution for pool ball impacts is approximately 0.95, and the coefficient of rolling friction between a pool ball and the cloth is μ, ≈ 0.01.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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What is the danger velocity, i.e. the initial velocity I would need to give the cue to pocket both balls? Based on what you know (and can research) about impacts and restitution, is your answer for this question likely to be (a) Greater than (b) Less than (c) About the same as the actual danger velocity in a real-world version of this scenario?
Transcribed Image Text:What is the danger velocity, i.e. the initial velocity I would need to give the cue to pocket both balls? Based on what you know (and can research) about impacts and restitution, is your answer for this question likely to be (a) Greater than (b) Less than (c) About the same as the actual danger velocity in a real-world version of this scenario?
I'm playing a game of pool with by brother; he's stripes. At some point, I notice I have a perfectly-aligned shot to put the 1-ball in the corner pocket. But I have to be careful; if I hit the cue too hard, I'll pocket my brother's ball as well. If my shot angle = 27°, and I've estimated the dimensions at the bottom (figure not to scale) in inches, how much initial velocity do I need to give the cue ball in order to pocket my ball but not my brother's? Reminder: the mass of a standard pool ball is 6 oz, the diameter is 2.25 inches, the coefficient of restitution for pool ball impacts is approximately 0.95, and the coefficient of rolling friction between a pool ball and the cloth is μ, ≈ 0.01. 7 12 50 8
Transcribed Image Text:I'm playing a game of pool with by brother; he's stripes. At some point, I notice I have a perfectly-aligned shot to put the 1-ball in the corner pocket. But I have to be careful; if I hit the cue too hard, I'll pocket my brother's ball as well. If my shot angle = 27°, and I've estimated the dimensions at the bottom (figure not to scale) in inches, how much initial velocity do I need to give the cue ball in order to pocket my ball but not my brother's? Reminder: the mass of a standard pool ball is 6 oz, the diameter is 2.25 inches, the coefficient of restitution for pool ball impacts is approximately 0.95, and the coefficient of rolling friction between a pool ball and the cloth is μ, ≈ 0.01. 7 12 50 8
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