A body with mass 5 kg is acted upon by a force `vec(F) = (- 3 hat (i) + 4 hat (j)) N`. If its initial velocity at t =0 is `vec(v) = 6 hat(i) - 12 hat (j) ms^(-1)`, the time at which it will just have a velocity along the y-axis is :

Options

A. never
B. 10s
C. 2s
D. 15s

Answer

B

Explanation

(b) Given mass, m=5 kg
Acting force,`F=(-3 hati+4 hatj)ms^(-1)`
Initial velocity at t=0,u=`(6 hati+12 hatj)ms^(-1)`
Retardation, `capa=(F)/(m)=(-(3hati)/(5)+(4hatj)/(5))ms^(-2)`
As final velocity is along Y-axis only, its x-component must be zero.
From v=u+at, for X-component only, `0=6hati-(3hati)/(5)t`
`t=(5xx6)/(3)=10s`