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Question

A graph of mass ejected vs time is shown in the figure below. [Given ln(5049)=0.02]


Find the velocity of the rocket after 5 s, if initial launch velocity is 200 m/s and velocity of ejected fuel w.r.t the rocket is 20 m/s. [Take g=10 m/s2 and initial mass of the rocket is 500 kg ].

A
20.4 m/s
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B
150.4 m/s
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C
30.4 m/s
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D
15.6 m/s
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Solution

The correct option is B 150.4 m/s
Given, Vo= initial launch velocity = 200 m/s
Vr= velocity of ejected fuel w.r.t rocket =20 m/s
m0= initial mass =200 kg
From the graph, rate of mass ejected
dMdt=μ=10050=2 kg/s

As we know, velocity after time t
V=Vogt+Vrln(mom)
Here, V=20010×5+20×ln[5005002×5]
=150+20×ln[5049]
=150+20×0.02
V=150.4 m/s

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