A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses t

Question

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 $g$, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is

Accepted Answer

From the equation of motion for a freely falling body initially at rest, the distance $s$ traversed in time $t$ is given by $s = \frac{1}{2}gt^2$. Rearranging for $g$, we get $g = \frac{2s}{t^2}$. The maximum percentage error in $g$ is the sum of the percentage error in $s$ and twice the percentage error in $t$. Therefore, $\% 	ext{ error in } g = \% 	ext{ error in } s + 2 	imes (\% 	ext{ error in } t) = e_1 + 2e_2$.

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