Two particles are fired from the same point, with speeds 100 m/s and 100 m/s, firing angles with horizontal = 60° and 120° respectively. The time after which their velocity vectors becomes perpendicular to each other, is
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Question

Two particles are fired from the same point, with speeds 100 m/s and 100 m/s, firing angles with horizontal = 60° and 120° respectively. The time after which their velocity vectors becomes perpendicular to each other, is

Options

G1 Physics · Accepted Answer

For the 60° projectile, v⃗₁ = 50î + (50√3 - 10t)ĵ. For the 120° projectile, v⃗₂ = -50î + (50√3 - 10t)ĵ. Perpendicular velocities require v⃗₁·v⃗₂ = 0: -2500 + (50√3 - 10t)² = 0. The first positive solution is t = 5(√3 - 1) s, which is option B. The printed source key marks option C, but at t = 5√3 s both vertical components are zero and the velocities are antiparallel, not perpendicular.