AS Daily A Level Physics question
Which statement must be true when a ball is thrown straight up with negligible air resistance? If the initial speed is doubled, what happens to (i) the time taken to reach the highest point and (ii) the maximum height reached? Choose the best pair and justify by proportional reasoning.
Answer
The correct answer is B.
Correct: B — Time to the top doubles; maximum height becomes four times larger. The acceleration is downward and constant, so the upward speed falls at a fixed rate; to reduce speed from 2u to 0 takes twice as long as from u to 0 (time ∝ u). The height to the top is the area under the v–t triangle up to v = 0, so h ∝ (1/2)u × t ∝ u × u = u^2, giving a factor of 4 when u is doubled. A is wrong because it assumes height scales linearly with launch speed; the v–t area shows a quadratic dependence. B is correct for constant downward acceleration: time ∝ u and height ∝ u^2. C is wrong because it swaps the scaling; time does not go as u^2. D is wrong because if the initial speed is larger, it takes longer for gravity to reduce it to zero; time cannot stay the same.