AS Daily A Level Physics question
In a safe lab drop test, a rubber ball is released from rest from 1.25 m above a soft mat. It takes about 0.50 s to reach the mat and its impact speed is about 4.9 m s^-1. Neglect air resistance and take g = 9.81 m s^-2. If the ball is instead dropped from 5.00 m (same conditions), which option best estimates the new fall time and impact speed?
Answer
The correct answer is A.
Correct: A — About 1.0 s; about 9.8 m s^-1 (both roughly double). From rest under constant g, both fall time and impact speed scale with the square root of height, so quadrupling height doubles each; numerically 0.50 s → ~1.0 s and 4.9 m s^-1 → ~9.8 m s^-1. B is wrong because if time doubles under the same g, the impact speed (v ≈ g t from rest) must also double, not stay similar. C is wrong because time does not scale linearly with height; quadrupling height doubles time, not quadruples it. D is wrong because the factor √2 applies to doubling the height, not quadrupling it; the given numbers correspond to a twofold, not fourfold, increase in height.