AS Daily A Level Physics question
On a calm day, a launcher fires two identical balls from level ground at the same initial speed u but at 30° (shot A) and 60° (shot B) above the horizontal. Air resistance is negligible. Which statement about their time in the air and their maximum height must be true? Use ratio reasoning based on vertical components.
Answer
The correct answer is C.
Correct: C — B stays in the air about 1.7 times as long as A, and B’s maximum height is three times A’s. Time in air depends on the upward vertical component (∝ sinθ), so TB/TA = sin60°/sin30° = (√3/2)/(1/2) ≈ 1.7; maximum height depends on the square of that component (∝ sin²θ), so HB/HA = (sin60°/sin30°)² = 3. A The factors 1.5 and 2 underestimate the true ratios; using sin and sin² gives ≈1.7 and 3. B Heights cannot be equal because the 60° launch has a larger upward component; squaring that component gives a larger height by a factor of 3. C Matches the correct sin and sin² ratios; a quick limiting check (0° gives near-zero time, 90° gives maximum time) confirms time increases with angle, so B lasts longer. D Times are not equal; equality is a misconception from the fact that complementary angles give the same range, not the same time.