A2 Daily A Level Physics question
A skydiver reaches a terminal speed of 55 m/s in a spread-eagle position. On a second jump they wear a training vest that makes their weight 20% greater, but they keep the same body position and area. At these speeds the resistive force of air is roughly proportional to the square of speed and to cross-sectional area. Which is the best estimate of the new terminal speed?
Answer
The correct answer is D.
Correct: D — It increases to about 60 m/s. At terminal speed, weight balances drag; with the same area the drag scales with the square of speed, so increasing weight by 20% makes terminal speed scale by √1.20 ≈ 1.10, giving about 55 × 1.10 ≈ 60 m/s. A assumes terminal speed is independent of mass, but a larger weight requires a higher speed before drag can balance it. B assumes terminal speed is directly proportional to weight (20% heavier → 20% faster), ignoring the square dependence that leads to a square-root change. C assumes a heavier skydiver falls slower, but with the same area the larger weight means a higher terminal speed, not a lower one. D correctly applies the square-root scaling from the v^2 dependence of drag with unchanged area.