AS Daily A Level Physics question
A ball is launched from ground level at 20 m/s in still air. Launch X uses an angle of 30° to the horizontal; Launch Y uses 60°. Both land back at the launch height. Without quoting equations by name, use component reasoning to decide which statement must be true.
Answer
The correct answer is B.
Correct: B — X and Y land the same distance away, but Y stays airborne about 73% longer than X. A ignores that time aloft is set by the vertical component: X has larger horizontal speed but smaller time, so the product (range) matches Y. B is correct because swapping 30° and 60° swaps horizontal and vertical components so range is unchanged while time ∝ vertical component, giving a ratio sin60°/sin30° ≈ 0.866/0.5 ≈ 1.73 (≈73% longer), and a quick limiting check (0° or 90° give zero range; symmetry about 45°) supports equal ranges. C is wrong because equal launch speed does not imply equal time aloft; only the vertical component controls ground-to-ground time. D is wrong because Y’s larger vertical component means a greater maximum height than X, and its range is not shorter under these conditions.