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. 10 s
C. 2 s
D. 15 s

Answer

B

Explanation

Given, mass = m = 5 kg
Acting force = F = `(-3hat(i) + 4hat(j))N`
Initial velocity at `t = 0 , u = (6hat(i) - 12 hat(j)) m//s`
Retardation `hat(a) = (F)/(m) = (-(3hat(i))/(5) + (4hat(j))/(5))m//s^(2)`
As final velcoity is along Y - axis only , its x - component must be zero
From v = u + at , for X - componen only , ` 0 =6 hat(i) - (3hat(i))/(5) t rArr t = (5 xx 6)/(3) = 10 s`