Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the graphs in the figure best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound af…

Question

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the graphs in the figure 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 = 10 m/s²) (The figures are schematic and not drawn to scale)

Accepted Answer

(1) Graph (a). While both are in the air, g cancels: y₂ - y₁ = (40 - 10)t = 30t, a straight line. First stone: -240 = 10t - 5t² ⇒ t² - 2t - 48 = 0 ⇒ t = 8 s. At that moment y₂ - y₁ = 240 m. After 8 s the first stone rests on the ground, so y₂ - y₁ = y₂ = 240 + 40t - 5t² measured from the ground: a parabola curving downward. It reaches zero when t² - 8t - 48 = 0, t = 12 s. Straight rise to 240 m at 8 s, then a concave-down fall to zero at 12 s: graph (a).

Step-by-step solution

Why the other options are wrong