AS Daily A Level Physics question
In a lab drop test, a steel ball is released from rest and falls vertically under gravity (take g = 9.81 m sā2; air resistance negligible). From a certain height, the average fall time is 0.50 s. The technician wants the fall time to be 20% longer while keeping everything else the same. Which change to the release height achieves this, to the nearest percent?
Answer
The correct answer is D.
Correct: D ā Increase the release height by 44%. For a drop from rest under constant g, the distance fallen is proportional to time squared, so making time 1.2 times larger makes height 1.2^2 = 1.44 times larger, i.e. a 44% increase. A assumes height is directly proportional to time (t ā h), which is incorrect here. B corresponds to a mistaken partial-squaring or rounding error; the required factor is 1.44, not 1.32. C assumes a simple linear scaling or rough doubling error; the correct square gives 44%, not 40%. D follows from h ā t^2, giving a 1.44 factor and hence a 44% increase.