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A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (take g = 10 m/s²)

  1. 75 m/s
  2. 55 m/s
  3. 40 m/s
  4. 60 m/s

Correct answer: 75 m/s

Solution

The first ball falls freely under gravity, so its displacement after 18 s is s₁ = (1/2)gt² = 0.5 × 10 × (18)² = 1620 m. The second ball is thrown after 6 s, so it falls for 12 s with an initial velocity v. Its displacement is s₂ = vt + (1/2)gt² = v(12) + 0.5 × 10 × (12)² = 12v + 720. Since they meet, s₁ = s₂, so 1620 = 12v + 720. Solving, v = 75 m/s.

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