Explanation Given information: The velocity ( v A ) of arrow A is ( 165 ft / s ) j+ ( 230 ft / s ) k . The velocity ( v B ) of ball B is ( 165 ft / s ) j+ ( 230 ft / s ) k . The weight of tennis ball A is 1.2 -oz . The weight of tennis ball B is 2 -oz Calculation: Consider the ball and arrow move together after the hit. Find the mass of arrow ( m A ) using the relation as follows: m A = w A g (1) Here, w A weight of arrow A and g is acceleration due to gravity. Substitute 1.2 -oz for w A and 32.2 ft / s for g in Equation (1). Ounce is unit weight of avoirdupois system, its equal to 1 16 pound . m A = 1.2 ( 1 16 ) 32.2 = 2.3292 × 10 − 3 slug Find the mass of arrow ( m B ) using the relation as follows: m B = w B g (2) Here, w B weight of arrow B . Substitute 2 -oz for w B and 32.2 ft / s for g in Equation (2). m B = 2 ( 1 16 ) 32.2 = 3.8820 × 10 − 3 slug According the conservation of momentum, total momentum is conserved. m A v A + m B v B = ( m A + m B ) v ¯ (3) Here, m A is mass of arrow A , m B is mass of arrow B , and v ¯ is velocity of after impact is v ′ . Substitute 2.3292 × 10 − 3 slug for m A , 3.8820 × 10 − 3 slug for m B , ( 165 ft / s ) j+ ( 230 ft / s ) k for ( v A ) , and ( 165 ft / s ) j+ ( 230 ft / s ) k for ( v B ) in Equation (3). [ ( 2.3292 × 10 − 3 × ( 165 ft / s ) j+ ( 230 ft / s ) k ) + ( 3.8820 × 10 − 3 × ( 165 ft / s ) j+ ( 230 ft / s ) k ) ] = [ 2

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 14.1, Problem 14.21P

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Find the position P where the tennis ball and arrow will hit the earth surface, relative to point O located directly under the point of impact.

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Chapter 14.1, Problem 14.20P

Chapter 14.1, Problem 14.22P

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Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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Find the position P where the tennis ball and arrow will hit the earth surface, relative to point O located directly under the point of impact.

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Find the position P where the tennis ball and arrow will hit the earth surface, relative to point O located directly under the point of impact.

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