AS Daily A Level Physics question
A lab dart launcher fires the same foam dart at a fixed muzzle speed of 12 m/s, once at 30° and once at 60° above the horizontal. The dart lands back at the launch height on level ground. Air resistance is negligible. Which statement must be true?
Answer
The correct answer is B.
Correct: B — Both shots land the same horizontal distance away, but the 60° shot stays in the air about 1.7 times as long. For fixed launch speed and level landing, horizontal range depends on the product of horizontal and vertical components, giving equal ranges for complementary angles (30° and 60°), while time of flight scales with the vertical component, so T60/T30 = sin60°/sin30° = (√3/2)/(1/2) = √3 ≈ 1.7; as a limiting check, steeper launches keep the dart in the air longer but don’t increase range beyond the 45° maximum. A The time does not simply double with angle, and the ranges are not halved vs doubled here; complementary angles give equal ranges, not a 2:1 difference. B This is correct because the vertical component (setting time) is larger at 60°, while the symmetric product of components yields the same range for 30° and 60°. C The 30° launch has a shorter time aloft (smaller vertical component) and does not travel farther than 60°; their ranges are equal for equal speed. D Time of flight depends on the vertical component, so it changes with angle; it is not the same for 30° and 60°.