An object falls freely from rest. It covers the same distance in last second. Which is covered in first 3 seconds, then in .............., it will reach the ground.

Options

A. 3s
B. 5s
C. 7s
D. 9s

Answer

B

Explanation

Suppose last second of free fall is n.
`therefore` Distance covered in `n^(th)` second,
`therefore In d _(n) = v _(0) + g/2 (2n -1) , v _(0) =0`
`therefore d _(n) = (10)/(2) (2n -1)`
`therefore d _(n) = 10 n -5 " "..(i)`
and distance covered in first three seconds,
`S_(3) = v _(0) t +1/2 g t ^(2) and v_(0) =0, t = 3s, g = 10 ms ^(-2)`
`therefore S_(3) =0 xx 3 + 1/2 xx 10 xx 9`
`therefore S_(3) = 45m" "...(ii)`
For given condition `d_(n) = S_(3)`
`therefore 10 n - 5=45`
`therefore 10n=50`
`therefore n = 5s`