A block of mass `m` in floating in a river flowing with a velocity of `2m//s`.A boat is moving behind the block with a velocity of `5m//s` with respect to the block as shown.From the boat a stone is thrown with a velocity `vecv=v_(1)hati-v_()hatj+v_(3)hatk` with respect to the river such that it hits the block.If `v_(1):v_(2):v_(3)=2sqrt3:2:3` then the velocity of the stone with respect to the ground is `(g=10m//s^(2))`

Options

A. `10hati-10/sqrt3hatj+5sqrt3hatk`
B. `12hati-10/sqrt3hatj+5sqrt3hatk`
C. `10hati-10hatj+5sqrt3hatk`
D. `10sqrt3hati-10/sqrt3hatj+5sqrt3hatk`

Answer

B

Explanation

Let `v_(1)=2sqrt3k v_(2)=2k v_(3)=3k, (2k)t=10`
`(3k)t-1/2xx10xxt^(2)=0,t=(3k)/5,k=5/sqrt3`
`vecv_(b)=vecv_(b//r)+vecv_(r)`