AS Daily A Level Physics question
On level ground, a student fires a foam dart from a launcher at 30° to the horizontal with speed u. Air resistance is negligible. They want to double the horizontal range but keep the launch angle the same. By what factor should they change the launch speed?
Answer
The correct answer is B.
Correct: B — Increase the speed by a factor of about 1.4. For a fixed launch angle on level ground and negligible air resistance, range is proportional to the square of launch speed, so doubling range requires the speed to be multiplied by √2 ≈ 1.41. A Overestimates: doubling speed would quadruple the range because range scales with speed squared. B This is the only factor that makes the squared term double (1.41^2 ≈ 2). C Incorrect because, at fixed angle, changing range requires changing speed; no change gives the same range. D Too small: a 1.2 factor gives only about 1.44 times the range (1.2^2 ≈ 1.44), not double.