Explanation Given information: The relative velocity is u = 5 , 400 ft / s . The change in velocity is v 1 − v 0 = 450 ft / s . The fuel consumed rate is W = 1 , 200 lb . Calculation: Calculate the gross weight of the spacecraft ( W 0 ) as shown below. W 1 = W 0 − W W 0 = W 1 + W Substitute 1 , 200 lb for W . W 0 = W 1 + 1 , 200 Sketch the Free Body Diagram of the spacecraft as shown in Figure 1. Refer to Figure 1. Apply the conservation of momentum to the fuel plus the fuel as shown below. m v = ( m − Δ m ) ( v + Δ v ) + ( Δ m ) ( v + Δ v − u ) m v = m v + m Δ v − Δ m v − Δ m Δ v + Δ m v + Δ m Δ v − Δ m u m Δ v − u Δ m = 0 Divide both sides of the Equation into Δ t as shown below. m Δ v Δ t − u Δ m Δ t = 0 m Δ v Δ t = u Δ m Δ t Δ v Δ t = u m Δ m Δ t Substitute − d m d t for Δ m Δ t . d v d t = − u m d m d t Integrate both sides of the Equation and apply the limits as shown below

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 14.3, Problem 14.98P

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The weight of the spacecraft after the firing.

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Chapter 14.3, Problem 14.97P

Chapter 14.3, Problem 14.99P

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Vector Mechanics for Engineers: Statics and Dynamics

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The weight of the spacecraft after the firing.

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The weight of the spacecraft after the firing.

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