AS Daily A Level Physics question
During two test jumps, the same 80 kg skydiver adopts two body positions. In position S he presents projected area A to the airflow; in position L he spreads out to present 1.20 A. The drag force from air is opposite the motion and is proportional to (area) × (speed)^2. Parachute is closed; ignore upthrust; air density is the same. Which statement must be true when comparing position L to S?
Answer
The correct answer is C.
Correct: C — Terminal speed decreases by about 9%, and the initial acceleration immediately after the jump is approximately g for both. At terminal speed, weight balances drag so mg ∝ A v_t^2, giving v_t ∝ 1/√A; increasing area by 20% makes v_t scale by 1/√1.20 ≈ 0.91 (about a 9% decrease). Immediately after the jump v ≈ 0, so drag ≈ 0; net force ≈ mg downward, hence a ≈ g for both. A … v_t does not fall by 20% because v_t depends on the square root of area, and the initial acceleration is not smaller than g at release. B … Terminal speed does change with area (larger area lowers v_t), and the initial acceleration at the instant of release is not less than g. C … Correct for both the quantitative ratio (1/√1.20) and the limiting case a ≈ g when v ≈ 0. D … Larger area reduces, not increases, terminal speed; and the initial acceleration is g for both positions, not only for the larger-area fall.