A is projected from origin with velocity (10î+20ĵ) m/s. Simultaneously B is projected from (30,40) m with velocity (4î+12ĵ) m/s. Both experience the same gravity. If their relative trajectories predict collision after N seconds, find N.
Physics · Kinematics part-3 Relative motion · Relative motion in 2-D and shortest distance problem
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Question

A is projected from origin with velocity (10î+20ĵ) m/s. Simultaneously B is projected from (30,40) m with velocity (4î+12ĵ) m/s. Both experience the same gravity. If their relative trajectories predict collision after N seconds, find N.

Physics · Kinematics part-3 Relative motion · Relative motion in 2-D and shortest distance problem

G1 Physics · Accepted Answer

r⃗_BA=(30−6t)î+(40−8t)ĵ because common gravity cancels. Both components vanish at t=5 s, so N=5 (subject to both particles remaining in physical flight).