AS Daily A Level Physics question
Two balls are launched from level ground at the same speed u: P at 30° and Q at 60° to the horizontal. Air resistance is negligible. Which statement must be true?
Answer
The correct answer is A.
Correct: A — They land the same horizontal distance away; the 60° launch is in the air about 1.7 times longer and reaches three times the maximum height of the 30° launch. A is correct because for equal launch speed the horizontal distance equals horizontal speed × time; complementary angles (30° and 60°) give the same product of horizontal and vertical components (same range), while time scales with sinθ (ratio ≈ sin60/sin30 = √3 ≈ 1.7) and maximum height with sin²θ (ratio 3). B is wrong because the maximum height does not match: it is larger for 60°, by a factor of 3, not equal. C is wrong because although the 60° launch has longer time and greater height, its smaller horizontal component cancels the extra time so the range is not greater but equal. D is wrong because the time aloft is not roughly the same (it’s about 1.7 times longer for 60°) and the height factor is 3, not 4.