AS Daily A Level Physics question
In a lab, a launcher fires the same ball from floor level at a fixed speed of 20 m/s. The first shot is at 50° above the horizontal; the second is at 60°, with the ball landing back at floor level and air resistance negligible. Which statement must be true when changing from 50° to 60°?
Answer
The correct answer is B.
Correct: B — Time of flight increases; horizontal range decreases. A time comparison uses the vertical component: time ∝ sinθ, so from 50° to 60° the factor is sin60/sin50 ≈ 0.866/0.766 ≈ 1.13 (about a 13% increase); range ∝ sin(2θ), so sin120/sin100 ≈ 0.866/0.985 ≈ 0.88 (about a 12% decrease). A Time of flight does not decrease (sin60 > sin50), and the horizontal range does not increase (sin120 < sin100). B states the correct changes: time increases (larger vertical component), while range decreases (2θ moves further past 90°, reducing sin(2θ)). C The range does not increase here because sin(2θ) falls from sin100 to sin120. D Time of flight is not unchanged; it increases because the vertical component of the launch speed is larger at 60°.