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Question

Two stones are thrown up simultaneously with initial speeds of u1 and u2 (u2>u1). They hit the ground after 6 s and 10 s respectively. Which of the following graphs correctly represents the time variation of Δx=(x2x1), the relative position of the second stone with respect to the first till 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


Up to the first 6 seconds, the positions of the two stones are given by
x1=u1t12gt2
and x2=u2t12gt2
Δx=x2x1=(u2u1)t
Since Δx varies linearly with t, the graph is a straight line till t = 6 s.
From t = 6 s to t = 10 s,
x1=0
and x2=u2t12gt2
Δx=x2x1=u2t12gt2
Thus (x2x1) versus t graph is not linear; it is a parabolic curve.
Now at t = 10 s, Δx=0
0=10u212×g×(10)2
u2=5g=50 ms1
Hence, from t = 6 s to t = 10 s, Δx=50t5t2.
Hence, the correct choice is (a).


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