Question

A ball falls from a tall bridge. The ball has a mass of 0.15 kg. The air density is 1.225 kg/m3
. The ball’s surface area is 0.0026 m2
. The ball’s coefficient of drag is 0.007. What is the ball’s terminal velocity?(1 point)
Responses

402 m/s

402 meters per second

363 m/s

363 meters per second

164 m/s

164 meters per second

30.4 m/s

Answer 1

Terminal velocity when drag balances weight: mg = 1/2 ρ C_d A v_t^2, so
v_t = sqrt( (2 m g) / (ρ C_d A) ).

Plugging in values:
v_t = sqrt( (2·0.15·9.81) / (1.225·0.007·0.0026) )
≈ sqrt(2.943 / 0.000022295)
≈ sqrt(132,080)
≈ 363 m/s.

Answer: 363 meters per second. (Note: this exceeds typical sound speed — the very small C_d used here makes the result unrealistic for a real falling ball.)