Question

A body of mass $5 \,kg $ starts from the origin with an initial velocity $\vec{u}$ $=\left(30 \hat{i}+40 \hat{j}\right)$ $m \, s^{-1}.$ If a constant force $\left(-6 \hat{i}-5\hat{j}\right) N$ acts on the body, the time in which the $y$ -component of the velocity becomes zero is

• A. $5 \,s$
• B. $20\, s$
• C. $40 \,s$
• D. $80\, s$

Answer 1

Answer: (C)

Here, $\vec{u} = (30 \hat{i} + 40 \hat{j})m\, s^{-1}, m = 5 kg$
$\vec{F} = ( - 6 \hat{i} - 5 \hat{j} ) N$
Acceleration,
$a = \frac{\vec{F}}{m} = \frac{-6 \hat{i} - 5\hat{j}}{5} = \left( -\frac{6 \hat{i}}{5} - \hat{j}\right) m \, s^{-2}$
The y component of velocity at any time t is given by
$ v_y = u_y + a_y t$
$u_y = 40 - 1 (t)$
According to given problem, $v_y = 0$
$\therefore \, t = 40 \, s$