AS Daily A Level Physics question
A skydiver of fixed mass falls vertically. Before opening a parachute, they eventually reach a terminal speed v1. The parachute is then opened, increasing the effective frontal area by a factor of 3 while everything else stays the same. Assume the resistive force of the air is proportional to frontal area multiplied by the square of the speed. Which statement must be true about the new terminal speed v2 compared with v1?
Answer
The correct answer is D.
Correct: D — v2 = v1/√3. At terminal speed, weight balances drag, and with drag proportional to area × speed², increasing area by 3 means speed must drop by √3 so that the product (area × speed²) stays the same. A assumes a linear inverse with area, which would only follow if drag increased directly with speed rather than with speed². B incorrectly treats the speed change as inverse to area squared, effectively applying the area factor twice. C ignores that increasing the area increases the drag at a given speed, so the terminal speed cannot remain the same. D follows from balancing the same weight against a drag that scales with area and the square of speed.