Question

Two stones are thrown up simultaneously from the edge of cliff 240 m high with initial speed of 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 ? Assume stones do not rebound after hitting the ground and neglect air resistance, take g 10m / s²)

Answer 1

Correct option (b)
Explanation :

Concept of relative motion can be applied to predict the nature of motion of one particle with respect to the other.

Consider the stones thrown up simultaneously as shown in the diagram below.

Considering motion of the second particle with respect to the first we have relative acceleration.

Thus, motion of first particle is straight line with respect to second particle till the first particle strikes ground at a time given by

- 240 = 10t - 1/ 2 x 10 x t²

or   t² - 2t - 48 = 0

or   t² - 8t + 6t - 48 =

or    t = 8 - 6   (not possible)

Thus, distance covered by second particle with respect to first particle in 8 s is

S₁₂ = (v₂₁) t = (40 - 10)(8s)

= 30 x 8 = 240m

Similarly, time taken by second particle to strike the ground is given by

Thus, after 8 s, magnitude of relative velocity will increase up to 12 s when the second particle strikes the ground.