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Question

Two stones are thrown up simultaneously with initial speeds u1 and u2(u2>u1). They hit the ground after 6 s and 10 s respectively. Which graph correctly represents the time variation of, Δx=(x2x1), the relative position of the second stone with respect to the first upto t=10 s?
Assume that the stones do not rebound after hitting the ground.

A
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B
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C
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D
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Solution

The correct option is A
Upto 6 s
urel=u2u1
arel=gg=0
Using second equation of motion, we get
Srel=urelt+12arelt2
Δx=(u2u1)×t
Initially relative acceleration between them is zero, so distance between them will increase linearly.
Hence, Δx increases linearly with t upto 6 s.
From t=6 s to t=10 s, first stone is at rest
arel=g
Δx=(u2u1)t12gt2 (in the downward journey Δx decreases parabolically)
Hence, the correct answer is option (a)

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