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

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