A student measures that distance traversed in free fall of a body, initially at rest in given time. He uses this data to estimated `g`, the acceleration due to gravity. If the maximum percentage error in measurement of the distance and the time are `e_(1)` and `e_(2)`, respectively, the percentage error in the estimation of `g` is

Options

A. `e_(1)+2e_(2)`
B. `e_(1)+e_(2)`
C. `e_(1)-2e_(2)`
D. `e_(2)-e_(1)`

Explanation

`h=(1)/(2)gt^(2)` (for free fall)
`g=(2h)/(t^(2))`
`(Deltag)/(g)=(Deltah)/(h)+(2Deltat)/(t)=e_(1)+2e_(2)`