With what velocity a ball be projected vertically so that the distance covered by it in `5^(th)` second is twice the distance it covers in its `6^(th)` second `(g=10 m//s^(2))`

Options

A. 58.8 m/s
B. 49 m/s
C. 64 m/s
D. 19.6 m/s

Answer

C

Explanation

Distance covered in nth second
`S_n = u + a/2 (2n-1)`
Given `S_5/S_6 = 2/1 `
`(u+((-g)/(2))(5 xx 2-1))/(u + ((-g)/(2))(2 xx 6 - 1)) = 2/1 rArr (2u-9g)/(2u -11g) = 2/`
`rArr 2u - 9g = 2 (2u - 11g)`
`rArr 2u -9g= 4u-22g`
`rArr 13g = 2u`
`rArr u = 6.5 = 63.7 m//s`