Explanation Given information: The initial velocity of ball A is 15 ft / s . The angle θ is 30 ° . Calculation: Write the velocity vectors as follows: v 0 = v 0 ( cos 30 ° i − sin30 ° j ) v A = − v A j v B = v B ( sin 30 ° i − cos 30 ° j ) v C = v C ( cos 30 ° i + sin30 ° j ) According to the conservation of momentum as follows: m v 0 = m v A + m v B + m v C (1) Substitute v 0 ( cos 30 ° i − sin30 ° j ) for v 0 , − v A j for v A , v B ( sin 30 ° i − cos 30 ° j ) for v B , and v C ( cos 30 ° i + sin30 ° j ) for v C in Equation (1). m ( v 0 ( cos 30 ° i − sin30 ° j ) ) = m ( − v A j ) + m ( v B ( sin 30 ° i − cos 30 ° j ) ) + m ( v C ( cos 30 ° i + sin30 ° j ) ) Equate i, j components. v 0 cos 30 ° = v B sin 30 ° + v C cos 30 ° (2) − v 0 sin 30 ° = − v A − v B cos 30 ° + v C sin 30 ° (3) Solving (2) and (3) Equation to get v B , v C . v B = 3 2 ( v 0 − v A ) v C = 1 2 ( v 0 + v A ) Express the conservation of energy as follows: 1 2 m v 0 2 = 1 2 m v A 2 + 1 2 m v B 2 + 1 2 m v C 2 (4) Divided by 1 2 m in Equation (4). v 0 2 = v A 2 + v B 2 + v C 2 (5) Substitute 3 2 ( v 0 − v A ) for v B and 1 2 ( v 0 + v A ) for v C in Equation (5)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.2, Problem 14.41P

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Find the magnitude of the velocities of ball A, B, and C.

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Chapter 14.2, Problem 14.40P

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Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3P Ch. 14.1 - Prob. 14.4P Ch. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9, assuming...

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Find the magnitude of the velocities of ball A , B , and C .

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