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  4. Velocity of a body on reaching the point, from which it was projected upwards, is

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Q. Velocity of a body on reaching the point, from which it was projected upwards, is

AIIMSAIIMS 1999Motion in a Plane

Solution:

Let the intial velocity of the body $=u$
And final velocity at the intial point be $v$.
Now the potential energy of the body at the point of projection is the same in both the upward and the downward journey. Since the total energy of the system has to be conscrved, the kinetic energies at that point must also be the same in both the journeys
$\therefore \frac{1}{2} m v^{2}=\frac{1}{2} m u^{2}$
$ \Rightarrow v=u$