A stone is dropped from rest. One second later another stone is projected vertically downward from the same point with speed 20 m s⁻¹. Taking g=10 m s⁻², find the time measured from the release of the first stone when the second overtakes it.
Physics · Kinematics Part-1 (one dimension) · Motion under gravity
JEE Mains NEET

Question

A stone is dropped from rest. One second later another stone is projected vertically downward from the same point with speed 20 m s⁻¹. Taking g=10 m s⁻², find the time measured from the release of the first stone when the second overtakes it.

Physics · Kinematics Part-1 (one dimension) · Motion under gravity

G1 Physics · Accepted Answer

Let downward displacement be positive and let t be measured from release of the first stone. First stone: y₁ = 5t². For t≥1, second stone: y₂ = 20(t−1) + 5(t−1)². Set y₁=y₂: 5t² = 20(t−1)+5(t−1)² ⇒ 5t² = 5t² + 10t − 15 ⇒ t = 1.5 s.