Two Objects Meeting Problem
From the top of a building a ball is dropped just as another ball is thrown up from the ground at 25 m/s, with g equal to 10 m/s², after how long do they meet if separated by 50 m?
Select the correct option:
Solution
2 s
Building on NCERT Class 11, Chapter 3 (Motion in a Straight Line), when two bodies move toward each other under gravity, the gravitational acceleration affects both identically, so their relative acceleration is zero and they approach at a constant relative velocity equal to the throw speed. The initial separation of 50 m therefore closes at 25 m/s, giving meeting time t = separation/relative velocity = 50/25 = 2 s. The option 2.5 s wrongly divides 50 by 20. The option 5 s ignores the upward ball's motion and uses only free fall through 50 m. The option 1.5 s underestimates by misapplying the relative velocity. Plausibility check: in 2 s the dropped ball falls (1/2)(10)(4) = 20 m, while the thrown ball rises 25(2) − (1/2)(10)(4) = 50 − 20 = 30 m; the sum 20 + 30 = 50 m exactly equals the initial separation, confirming they meet at t = 2 s.
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- two objects meeting problem
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
2 s
Building on NCERT Class 11, Chapter 3 (Motion in a Straight Line), when two bodies move toward each other under gravity, the gravitational acceleration affects both identically, so their relative acceleration is zero and they approach at a constant relative velocity equal to the throw speed. The initial separation of 50 m therefore closes at 25 m/s, giving meeting time t = separation/relative velocity = 50/25 = 2 s. The option 2.5 s wrongly divides 50 by 20. The option 5 s ignores the upward ball's motion and uses only free fall through 50 m. The option 1.5 s underestimates by misapplying the relative velocity. Plausibility check: in 2 s the dropped ball falls (1/2)(10)(4) = 20 m, while the thrown ball rises 25(2) − (1/2)(10)(4) = 50 − 20 = 30 m; the sum 20 + 30 = 50 m exactly equals the initial separation, confirming they meet at t = 2 s.
This hard difficulty physics question is from the chapter kinematics, covering the topic of two objects meeting problem. It appeared in the 2025 exam.
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