AS Daily A Level Physics question
From ground level, a student launches the same foam dart twice with the same initial speed: first at 30° above the horizontal, then at 60°. Air resistance is negligible and the dart lands back at launch height each time. Which statement must be true about the horizontal range R and time of flight T of the two shots? Use component reasoning and, if needed, a quick ratio estimate with sin60 ≈ 0.87 and sin30 = 0.50.
Answer
The correct answer is B.
Correct: B — The ranges are equal, but the 60° shot stays in the air about 1.7 times as long. Time depends on the vertical component (proportional to sinθ), so T60/T30 ≈ 0.87/0.50 ≈ 1.7; range depends on horizontal × time, giving sinθ cosθ, which is the same for 30° and 60° (complementary angles), consistent with the 45° limiting case for maximum range. A is wrong because it assumes a longer time must mean a longer range, ignoring that the 60° shot has a smaller horizontal component that exactly offsets the longer time. B is correct because complementary angles produce equal sinθ cosθ (equal ranges) while the larger sin60 makes the flight last about 1.7 times longer. C is wrong because keeping speed the same does not keep components the same: time changes with sinθ, so T differs even though speed is unchanged. D is wrong because time and peak height are set by the vertical component, which is larger at 60°, not 30°; the 30° shot has greater horizontal speed but a shorter time and a lower peak.