(a) Explanation Given information: Consider the mass of ball A , ball B , and C is denoted by m . The initial velocity of the ball is v 0 = 12 ft/s . The initial velocity of the ball B and C is zero. Consider the final velocity of ball A and B are denoted by v A and v B . The final velocity of the ball C is v C = 6.29 ft/s . Calculation: Show the collision of the ball A , B , and C as shown in Figure 1. Refer Figure 1. Show the conservation of momentum in x -direction as follows: m v 0 cos 30 ° = m v A sin 7.4 ° + m v B sin 49.3 ° + m v C cos 45 ° m v 0 cos 30 ° = m ( v A sin 7.4 ° + v B sin 49.3 ° + v C cos 45 ° ) 0.866 m v 0 = m ( 0.1288 v A + 0.75813 v B + 0.7071 v C ) 0.866 v 0 = 0.1288 v A + 0.75813 v B + 0.7071 v C Substitute 6.29 ft/s for v C and 12 ft/s for v 0 . 0.866 ( 12 ) = 0.1288 v A + 0.75813 v B + 0.7071 ( 6.29 ) 10.392 = 0.1288 v A + 0.75813 v B + 4.447 0.1288 v A + 0.75813 v B = 5 (b) To determine Find the magnitude of velocity of ball B .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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, Problem 14.108RP

(a)

To determine

Find the magnitude of velocity of ball A.

(b)

To determine

Find the magnitude of velocity of ball B.

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Chapter 14, Problem 14.107RP

Chapter 14, Problem 14.109RP

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the magnitude of velocity of ball A .

Solution Summary: The author shows the magnitude of velocity of the ball A, B, and C as shown in Figure 1.