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

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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Concept explainers

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

Question

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

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