AS Daily A Level Physics question
On level ground in still air, a student launches the same ball twice from the same point with the same speed but at two angles above the horizontal: θ and 90° − θ. Neglect air resistance. Which statement must be true?
Answer
The correct answer is C.
Correct: C — The horizontal ranges are the same, but the times of flight are different except when θ = 45°. A higher-angle shot has a larger vertical component (longer airtime) but a smaller horizontal component, while the lower-angle shot has the opposite; these effects balance so the ranges match, but the times generally differ unless both angles are 45°. A is wrong because different angles give different vertical components, so maximum heights and usually times of flight are not the same. B is wrong because it reverses the truth: the ranges match for complementary angles, whereas the times of flight do not (except at 45°). C is correct because complementary angles swap horizontal and vertical components so the product “horizontal speed × time in air” is the same, but the times only match when θ = 45°. D is wrong because although the larger angle often increases airtime, it does not increase range; in the limit as θ approaches 90°, the range tends to zero.