Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speeds 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?

For the first ball, 240=10t - (1/2)gt² ≅ 5t² - 10t - 240 = 0 ⇒ t² - 2t - 48 = 0 ⇒ t=8, -6. The 1st particle will reach the ground in 8 secs. Upto 8 secs, the relative velocity between the particles is 30m/sec and the relative acceleration is zero. For the 2nd particle, 240=40t - (1/2)gt² ⇒ t² - 8t - 48 = 0 ⇒ t=12 secs. The second particle will strike the ground in 12 secs. Option(A): Linear behaviour after 8 secs, hence can be eliminated. Option(B) shows increase until 12 secs, hence is not correct. after 8 secs, separation will decrease. Option(c) is the correct one.