KVPY 2020-21 SA Exam Previous Papers

Question : 19 of 80

Marks: +1, -0

A spacecraft which is moving with a speed u relative to the earth in the x-direction, enters the gravitational field of a much more massive planet which is moving with a speed 3u in the negative x-direction. The spacecraft exists following the trajectory as shown below.

The speed of the spacecraft with respect to the earth a long a time after it has escaped the planet’s gravity is given by

Validate

Solution:

From conservation of angular momentum

mv_1r = mv_2r

Initial velocity of spacecraft w.r.t. planet

({v}↖{→}_{s \/ p})_{\text "initial "}=4 u

Final velocity of the spacecraft w.r.t. planet

({v}↖{→}_{s \/ p})_{\text "final "}=-4 u

Now,

{v}↖{→}_{S \/ E}={v}↖{→}_{S \/ P}-{v}↖{→}_{E \/P}

= –4u – (3u) = – 7u
Hence, speed of spacecraft w.r.t. earth finally becomes 7u

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