Explanation Given information: The weight ( W m ) of the man is 180 lb . The weight ( W w ) of the woman is 120 lb . The weight ( W b ) of the boat is 300 lb Calculation: Sketch the diagram for woman dives first as shown in Figure 1. Refer to Figure 1. Determine the velocity of the boat if the woman dives first. Applying conservation of momentum, − m w ( 16 − v 1 ) + ( m b + m m ) v 1 = 0 − w w g ( 16 − v 1 ) + ( w b + w m g ) v 1 = 0 (1) Here, m w is mass of woman, m m is mass of man, v 1 is velocity of boat, and m b is mass of boat. Substitute 120 for m w and 300 + 180 for ( m b + m m ) in Equation (1). − 120 g ( 16 − v 1 ) + ( 300 + 180 g ) v 1 = 0 − 1 , 920 + 120 v 1 + 300 v 1 + 180 v 1 = 0 − 1 , 920 + 600 v 1 = 0 v 1 = 3.2 ft / s Therefore, the ( 16 − v 1 ) is 12.80 ft / s . The kinetic energy before dive T 0 is 0. Find the kinetic energy after dive using the relation as follows: T 1 = 1 2 m b + m m g ( v 1 ) 2 + 1 2 m w g ( v ) 2 = 1 2 w b + w m g ( v 1 ) 2 + 1 2 w w g ( v ) 2 (2) Substitute 120 for m w , 300 + 180 for ( m b + m m ) , 3.2 ft / s for v 1 , 12.80 ft / s for v , and 32.2 ft / s 2 in Equation (2). T 1 = 1 2 300 + 180 32.2 ( 3.20 ) 2 + 1 2 120 32.2 ( 12.80 ) 2 = 76.32 + 305.29 = 381.61 ft ⋅ lb Find the work done by the woman as follows: work done = T 1 − T 0 (3) Substitute 381.61 ft ⋅ lb for T and 0 for T 0 in Equation (3). work done= 381.61 − 0 = 382 ft ⋅ lb Thus, the work done by the Woman is 382 ft ⋅ lb _ Man dives next: Sketch the diagram man dives next as shown in Figure 2

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 14.2, Problem 14.33P

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