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

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 14.3, 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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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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The weight of the spacecraft after the firing.

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