AS Daily A Level Physics question
In a lab test, two identical steel spheres are released from rest onto the same floor: one from 1.25 m and the other from 5.00 m. Air resistance is negligible; take g = 9.81 m s^-2. Compared with the 1.25 m drop, what happens for the 5.00 m drop to (i) the time of fall and (ii) the impact speed?
Answer
The correct answer is D.
Correct: D — Time doubles and impact speed doubles. A 5.00 m is four times 1.25 m, and for free fall from rest both time and speed scale with the square root of height, so each increases by √4 = 2. A assumes both quantities scale linearly with height, which is incorrect because they scale with the square root. B has the right factor for speed but incorrectly makes time scale linearly instead of with the square root. C assumes impact speed is independent of drop height, ignoring that v ∝ √h. D matches t ∝ √h and v ∝ √h: quadrupling h doubles both t and v.