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=(x2−x1), 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.
Up to the first 6 seconds, the positions of the two stones are given by
Since Δx varies linearly with t, the graph is a straight line till t = 6 s.
From t = 6 s to t = 10 s,
Thus (x2−x1) versus t graph is not linear; it is a parabolic curve.
Now at t = 10 s, Δx=0
Hence, from t = 6 s to t = 10 s, Δx=50t−5t2.
Hence, the correct choice is (a).