AS Daily A Level Physics question
From a balcony 20 m above level ground, two identical steel balls are released at the same instant. Ball A is thrown straight down at 5.0 m s^-1; Ball B is thrown straight up at 5.0 m s^-1. Air resistance is negligible and take g = 9.81 m s^-2 downward. Which statement must be true about the times to reach the ground and the impact speeds?
Answer
The correct answer is D.
Correct: D — Ball B takes about 1.6 times longer than A to arrive, but both have the same impact speed magnitude. A Equal g does not mean equal arrival times when the initial velocities differ in direction and sign; the upward throw adds extra time before descending. B The time ratio is not 2 (solving s = ut + 0.5gt^2 gives t_A ≈ 1.58 s and t_B ≈ 2.59 s, ratio ≈ 1.6), and the impact speeds are not different just because A started downward. C While B does take longer, the impact speed magnitudes are equal because v^2 depends on u^2 and the drop distance (same 20 m), so the sign of the initial velocity doesn’t change the final speed magnitude. D Using downward as positive, A: 4.905 t^2 + 5t − 20 = 0 → t_A ≈ 1.58 s; B: 4.905 t^2 − 5t − 20 = 0 → t_B ≈ 2.59 s (about 1.6× longer), and v^2 = u^2 + 2gs gives v ≈ √(25 + 2×9.81×20) ≈ 20.5 m s^-1 for both; in the limiting case u → 0 these times converge, consistent with this result.