Projectile Motion
A ball is projected horizontally from a cliff with a speed of 15 m/s and lands after 3 seconds, with g equal to 10 m/s², what is its horizontal range?
Select the correct option:
Solution
45 m
As explained in NCERT Class 11, Chapter 4 (Motion in a Plane), horizontal projectile motion has two independent components: a constant horizontal velocity and a vertical motion governed by gravity. The horizontal range equals the horizontal velocity multiplied by the time of flight, since there is no horizontal acceleration. Here the horizontal velocity stays 15 m/s throughout, and the time of flight is given as 3 s, so range R = 15 × 3 = 45 m. The option 30 m wrongly uses only 2 s of flight time. The option 60 m incorrectly adds a contribution from gravity to the horizontal direction, which does not happen. The option 15 m mistakenly equates range to the launch speed alone, ignoring time. Plausibility check: the vertical drop in 3 s would be (1/2)(10)(9) = 45 m, a physically reasonable cliff height, and since horizontal speed is unchanged, 45 m horizontal range is consistent with independent component motion.
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About This Question
- Subject
- physics
- Chapter
- kinematics
- Topic
- projectile motion
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
45 m
As explained in NCERT Class 11, Chapter 4 (Motion in a Plane), horizontal projectile motion has two independent components: a constant horizontal velocity and a vertical motion governed by gravity. The horizontal range equals the horizontal velocity multiplied by the time of flight, since there is no horizontal acceleration. Here the horizontal velocity stays 15 m/s throughout, and the time of flight is given as 3 s, so range R = 15 × 3 = 45 m. The option 30 m wrongly uses only 2 s of flight time. The option 60 m incorrectly adds a contribution from gravity to the horizontal direction, which does not happen. The option 15 m mistakenly equates range to the launch speed alone, ignoring time. Plausibility check: the vertical drop in 3 s would be (1/2)(10)(9) = 45 m, a physically reasonable cliff height, and since horizontal speed is unchanged, 45 m horizontal range is consistent with independent component motion.
This medium difficulty physics question is from the chapter kinematics, covering the topic of projectile motion. It appeared in the 2025 exam.
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