385_Dynamics 11ed Manual

# 385_Dynamics 11ed Manual - s 2 m 2 ⋅ = Solution m M C M F...

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Engineering Mechanics - Dynamics Chapter 15 a F M = a 0.53 m s 2 = Problem 15-118 The rocket car has a mass M C (empty) and carries fuel of mass M F . If the fuel is consumed at a constant rate c and ejected from the car with a relative velocity v DR , determine the maximum speed attained by the car starting from rest. The drag resistance due to the atmosphere is F D = kv 2 and the speed is measured in m/s. Units Used: Mg 10 3 kg = Given: M C 3Mg = M F 150 kg = v DR 250 m s = c 4 kg s = k 60 N
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Unformatted text preview: s 2 m 2 ⋅ = Solution: m M C M F + = At time t the mass of the car is m ct − Set F k v 2 = , then k − v 2 m ct − ( ) t v d d v DR c − = Maximum speed occurs at the instant the fuel runs out. t M F c = t 37.50 s = Thus, Initial Guess: v 4 m s = Given v v 1 cv DR kv 2 − ⌠ ⎮ ⎮ ⎮ ⌡ d t t 1 m ct − ⌠ ⎮ ⎮ ⌡ d = v Find v ( ) = v 4.06 m s = 383...
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