AS Daily A Level Physics question
A student throws a ball straight up from ground level. As it passes the level of a balcony 15 m above the ground, a motion sensor measures its speed as 10 m/s upward. Ignore air resistance and take g = 9.81 m s−2. Which statement must be true about the next time the ball passes the balcony level?
Answer
The correct answer is D.
Correct: D — About 2.0 s later, with speed equal to 10 m/s downward. From the balcony level the ball decelerates from 10 m/s to 0 in about 10/9.81 ≈ 1.02 s, then accelerates back to 10 m/s downward in the same time; total ≈ 2.04 s, and symmetry (or constant-g energy change) gives the same speed magnitude on return but downward. A The 1.0 s estimate halves the correct time and assumes it gains extra speed by the balcony, but at the same height the speed magnitude matches the earlier value if air resistance is negligible. B The 1.0 s time comes from ignoring that the upward and downward legs each take ~1.02 s, so this underestimates the interval by a factor of two. C The ~2.0 s timing is right, but claiming a smaller speed magnitude contradicts constant-g symmetry: returning to the same height gives the same speed magnitude. D This matches both the time (2×10/9.81) and the direction (downward) with the correct speed magnitude.