Two stones are thrown vertically upwards simultaneously with their initial velocities ${"mathml":"<math class="image_resized" style="width:16px;height:12px"><span style="font-family:$ and ${"mathml":"<math class="image_resized" style="width:16px;height:12px"><span style="font-family:$ respectively. Prove that the heights reached by them would be in the ratio of :

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u 12 : u 22

u 1 : u 2

u 22 : u 22

u 2 : u 1

answer is A.

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Detailed Solution

Concept: Assume accelerations of (-g) upward and (+g) downward. Use a kinematic equation to answer this question.
Consider the ultimate velocity of both stones to be zero, and keep in mind that the initial velocity must vary.
We know for upward motion,

But at highest point

Therefore,

For first ball,

And for second ball

Thus,

Hence, the correct option is 1.

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