Two particles A and B are projected simultaneously from points on horizontal ground separated by 100 m towards each other. Particle A is projected at 45° with 25√2 m/s and particle B at 45° with 25√2 m/s. At what time t will they collide if their horizontal trajectories lie in the same vertical plane?

Answer and explanation

Correct answer: B. 2.0 seconds

  1. Step 1: Both particles have horizontal speed 25√2 · cos 45° = 25 m/s, and they move towards each other.
  2. Step 2: The horizontal gap of 100 m closes at 25 + 25 = 50 m/s.
  3. Step 3: Both also have vertical speed 25 m/s and the same acceleration g, so they are always at the same height; they meet when the horizontal gap reaches zero.
  4. Step 4: t = 100 / 50 = 2.0 s (both are still in the air, since each flight lasts about 5 s).
Answer
2.0 seconds.
Why not the others: 1.5 s, 2.5 s and 3.0 s would need a closing speed of about 67, 40 and 33 m/s, which does not match 25 + 25 = 50 m/s.

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