AS Daily A Level Physics question
In a school lab, a student films a ball dropped vertically from rest. From 5.0 m the impact speed is measured to be about 9.9 m s^-1. Taking g = 9.81 m s^-2 and ignoring air resistance, what impact speed should be expected if the ball is dropped from 20 m?
Answer
The correct answer is D.
Correct: D — 19.8 m s^-1. For drops from rest with constant g, impact speed scales with the square root of height, so v ∝ √h; increasing height from 5.0 m to 20 m is a factor of 4, so speed doubles: 2 × 9.9 ≈ 19.8 m s^-1. A 9.9 m s^-1 — Wrong: constant g does not mean the same final speed; greater distance allows more speeding up. B 14 m s^-1 — Wrong: this corresponds roughly to a √2 increase (about doubling the height), not quadrupling it. C 39 m s^-1 — Wrong: assumes speed is proportional to height; the relationship is square-root, not linear. D 19.8 m s^-1 — Correct because √(20/5) = √4 = 2, so the speed doubles.