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Question

A body A is projected upwards with velocity v1. Another body B of same mass is projected at an angle of 450 with the horizontal. Both reach the same height. What is the ratio of their initial kinetic energies?

A
1/4
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B
1/3
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C
1/2
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D
1
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Solution

The correct option is B 1/2
Let the velocity of body A is v1 and mass is m
Let Velocity of body B is v2 and mass is m and it is projected at angle of 45o with the horizontal$

Maximum height reached by A, h1=v212g

Maximum height reached by B, h2=v22 sin245o2g

Given that h1=h2

v212g=v22 sin245o2g

v21v22=12

Hence Required ratio of their initial kinetic energy, K.E.1K.E.2=12mv2112mv22=v21v22=12

Hence option (C) is correct.


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