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Question

A rocket is launched to travel vertically upward with a constant velocity of 20 m/s. After travelling for 35 seconds, the rocket develops a snag and its fuel supply is cut off. The rocket then travels like a free body. The height achieved by it is:

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Solution

We know that
S=ut+12at2

Since, it is moving at a constant velocity.

So,
S=ut

After 35 seconds the distance will be
S=20×35=700 m

Now.
From 700 m above the ground now it travels at a free fall.

The initial velocity =20 m/s

Final velocity =0

Acceleration due to gravity =10

Now,

V2=U22gS
0=40020S
20S=400
S=20 m

The total height achieved
=700+20
=720 m

Time it takes to drop back to the earth is
S=ut+0.5×gt2

But u=0

So,
720=0.5×10×t2
720=5t2
t2=144
t=12 seconds

The total time it takes is
12+35=47 seconds

Hence, this is the answer.

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