Two particles are projected simultaneously from the same point with the same speed 20 m/s, one at 30° and the other at 60° above the horizontal, both in the same vertical plane and in the same horizontal direction. Neglect air resistance. The distance between them after 1 s is:
Options

Question

Two particles are projected simultaneously from the same point with the same speed 20 m/s, one at 30° and the other at 60° above the horizontal, both in the same vertical plane and in the same horizontal direction. Neglect air resistance. The distance between them after 1 s is:

Options

G1 Physics · Accepted Answer

Both particles have the same gravitational acceleration, so their relative acceleration is zero. Their separation after time t equals |Δu|t. Δuₓ = 20(cos60° - cos30°) = -10(√3 - 1), and Δuᵧ = 20(sin60° - sin30°) = 10(√3 - 1). Hence |Δu| = 10√2(√3 - 1) m/s. At t = 1 s, separation = 10√2(√3 - 1) m. Therefore option B is correct.