AS Daily A Level Physics question
In a simple drop-test rig, a steel ball is released from rest from 0.80 m and the speed just before impact is about 4.0 m/s (consistent with taking g = 9.81 m/s^2 and negligible air resistance). The team wants to increase the impact speed by 50% while still dropping from rest. Which new drop height is closest to what they need?
Answer
The correct answer is C.
Correct: C — 1.80 m. For a drop from rest with constant g, impact speed scales with the square root of height, so to increase speed by a factor 1.5 the height must be multiplied by (1.5)^2 = 2.25; 0.80 m × 2.25 ≈ 1.8 m. A assumes speed increases in direct proportion to height (v ∝ h), so a 50% speed increase would need only 50% more height, which is incorrect because v ∝ √h. B reflects mixing up the square and square root, effectively multiplying the height by √1.5 instead of (1.5)^2, which underestimates the required height. C uses the correct ratio reasoning: v ∝ √h, so h must scale with the square of the speed factor. D quadruples the height, which would double the speed (a 100% increase), not a 50% increase.