Question

A body of mass $5kg$ 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. $5s$
• B. $20s$
• C. $40s$
• D. $80s$

Answer 1

Answer: (C)

Here, $\vec{u}=(30\hat{i}+40\hat{j})m{s}^{-1},m=5kg$
$\vec{F}=(-6\hat{i}-5\hat{j})N$
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, $v_y=0$
$\therefore t=40s$