AS Daily A Level Physics question
From a balcony 15 m above the ground, ball P is released from rest. Half a second later, ball Q is thrown straight down from the same point so that both balls land at the same time. Neglect air resistance and take g = 9.81 m s^-2. What initial speed must ball Q have?
Answer
The correct answer is D.
Correct: D — 5.9 m s^-1 downward. Time for P: t ≈ sqrt(2h/g) = sqrt(30/9.81) ≈ 1.75 s, so Q has about 1.25 s; using s = ut + 1/2 g t^2 gives u = [15 − 0.5×9.81×(1.25)^2]/1.25 ≈ 5.9 m s^-1 downward. A uses u ≈ s/t and ignores the 1/2 g t^2 term, overestimating to about 12 m s^-1. B likely assumes t ≈ 1 s or rounds g to 10, undercounting the distance gained from acceleration and giving ~10 m s^-1. C matches the dropped ball’s impact speed (~sqrt(2gh) ≈ 17 m s^-1), forgetting that gravity continues to add speed to Q during its shorter flight. D is the only value consistent with the shorter available time and the extra distance contributed by acceleration.