Question

A particle is projected with velocity of $u=30\hat{i}+40\hat{j}$ . Its velocity (in $m/s$) after $2$ seconds is
(Take $g=10m/s^2$)

• A. $10\sqrt{13}$
• B. $20\sqrt{13}$
• C. $\sqrt{13}$
• D. $13\sqrt{10}$

Answer 1

The correct option is A $10\sqrt{13}$

Component of projected velocity in $x$ and $y$ directions are $u_x=30m/s$ and $u_y=40m/s$
From first equation of motion in $y$- direction
$v_y=u_y-gt=40-\left(10\right)\left(2\right)=20m/s$
And $x$- direction velocity remains constant during flight,
$v_x=u_x=30m/s$
Hence, its velocity after $2s$ is $v=\sqrt{{30}^2+{20}^2}=10\sqrt{13}m/s$