A ball is released from rest at a point 1.80m above the laboratory floor. Just before the ball strikes the floor, it passes through a velocity sensor that records its speed as 5.94ms−1 with an uncertainty of ±0.05ms−1.
a. (a) Prove mathematically that, for a body released from rest and falling freely through a distance h, the acceleration due to gravity g can be expressed in terms of the final speed v as g=2hv2.
b. (b) Using the given data, calculate the experimental value of g.
c. (c) Determine the maximum percentage error in the value of g arising solely from the uncertainty in the speed measurement.
d. (d) Briefly comment on whether measuring speed at impact or measuring time of fall would generally lead to a smaller percentage error for the same drop height, giving one reason for your answer.