A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate , the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are and respectively, the percentage error in the estimation of is
From the equation of motion for a freely falling body initially at rest, the distance traversed in time is given by . Rearranging for , we get . The maximum percentage error in is the sum of the percentage error in and twice the percentage error in . Therefore, .
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