Explanation Given: The weight of the missile is W = 4000 lb . The constant thrust provided by the turbo jet engine is T = 15000 lb . The fuel burned at the rate of 150 lb/s . The velocity of the exhaust gas relative to the missile is v D / e = 3000 ft/s . The initial velocity of the missile is 300 mi/h . Draw the free body diagram of the missile as shown in Figure (1). Consider the loss masses only. Write the equation of propulsion with variable mass. ∑ F c v = m d v d t + v D / e d m e d t (I) Here, ∑ F c v is the resultant of all forces acting in control volume d v d t is the rate of change of velocity with respect to time, v D / e is the velocity of the system moving with ejected mass and d m e d t is the rate of mass ejected. Conclusion: The initial mass of the system is m 0 = W 32.2 ft/s 2 Substitute 40000 lb for W . m 0 = 40000 lb 32.2 ft/s 2 = 1242.2360 slug Calculate the rate of mass ejected from the system ( c ) by the two turbo jet engines. c = 2 d m e d t = 2 ( 150 lb/s × 1 32.2 ft/s 2 ) = 9.3168 slug/s Calculate the total mass of the at the time t . m = m 0 − c t Refer Figure (1). Calculate the resultant force of all the forces acting on the control volume. ∑ F c v = T . Calculate the velocity of the missile. Substitute T for ∑ F c v , m 0 − c t for m and c for d m i d t in Equation (I). T = ( m 0 − c t ) d v d t − v D / e ( c ) ( m 0 − c t ) d v d t = T + v D / e c d v = T + v D / e c m 0 − c t d t (II) Integrate the Equation (II) at the limits of v = v 0 to v and t = 0 to t

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 15.9, Problem 139P

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The velocity of the missile after the 4 s burn time of the boosters:

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Chapter 15.9, Problem 138P

Chapter 15.9, Problem 140P

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Engineering Mechanics: Dynamics (14th Edition)

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The velocity of the missile after the 4 s burn time of the boosters:

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