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  4. Two stones are thrown up simultaneously from the edge of cliff with initial speeds v and 2v . The relative position of the second stone with respect to first varies with time till both the stones strike the ground as

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Q. Two stones are thrown up simultaneously from the edge of cliff with initial speeds $v$ and $2v$ . The relative position of the second stone with respect to first varies with time till both the stones strike the ground as

NTA AbhyasNTA Abhyas 2022

Solution:

Initially when both are in air, the relative acceleration between them is zero. Therefore, relative position verus-time graph is a straight line.
$S_{1}=vt-\frac{1}{2}gt^{2}$
$S_{2}=2vt-\frac{1}{2}gt^{2}$
$S_{21}=S_{2}-S_{1}$
$S_{21}=vt$
Once the first ball reaches the ground, its acceleration becomes zero. Therefore, the relative acceleration is now g and the graph is parabolic.
$S_{2}=2vt-\frac{1}{2}gt^{2}$