AS Daily A Level Physics question
Two identical balls are released simultaneously from a balcony 10 m above level ground. Ball A is thrown straight down at 5.0 m/s; Ball B is thrown straight up at 5.0 m/s from the same point. Air resistance is negligible. Take g = 9.81 m s^-2. Which statement must be true?
Answer
The correct answer is A.
Correct: A — They hit the ground with the same speed, and Ball B takes about twice as long as Ball A to hit the ground. A Using downward as positive, the ground impact speed satisfies v^2 = u^2 + 2gh, so v = sqrt(5.0^2 + 2×9.81×10) ≈ 14.9 m/s for both; times are t_A = (v − 5.0)/9.81 ≈ 1.01 s and t_B = (v + 5.0)/9.81 ≈ 2.03 s, so B takes about twice as long; as u → 0 the times converge, consistent with the drop limit. B The impact speeds are the same but the longer time is for the ball thrown upward, not the one thrown downward; the ratio (v + u)/(v − u) ≈ 2.0 is reversed here. C Throwing upward increases the time, not decreases it, and the impact speed is determined by u^2 + 2gh, which is the same for ±u, so B does not hit sooner nor faster. D The impact speed does not depend on the sign of u (only u^2), and equal arrival times would require u = 0; with u = 5.0 m/s, the times differ as t_B > t_A.