AS Daily A Level Physics question
A bench-top launcher in a physics lab fires a steel ball at a fixed speed u. With the barrel set to 30° above the horizontal, the ball lands back at the same height as launch. The launcher is then set to 60° with the same speed u, again landing at the same height. Air resistance is negligible. Which statement must be true about the second shot compared with the first?
Answer
The correct answer is B.
Correct: B — Time increases by a factor of about 1.7; range is unchanged. Time of flight depends on the vertical component (T ∝ sinθ), so T60/T30 = sin60°/sin30° = (0.866)/(0.5) ≈ 1.73; range for level launch/landing depends on both components via R ∝ sin2θ, and sin120° = sin60°, so the range is the same; a useful check is that complementary angles give equal ranges (30° and 60°). A is wrong because the larger upward component at 60° increases time (not unchanged) and the range is not halved for complementary angles. B states the correct comparison from component reasoning (T ∝ sinθ, R ∝ sin2θ). C is wrong because the time factor is √3 ≈ 1.73, not 2, and the suggested range change mixes up horizontal speed with the compensating longer time. D is wrong because, although the time increases by about 1.7, the range does not halve; complementary angles at the same speed give equal ranges.