Question

A projectile is thrown horizontally with a speed of $20{\text{m s}}^{-1}$. If $g$ is $10{\text{ms}}^{-2}$, then the speed of the projectile after $5$ seconds will be nearly

• A. $0.5{\text{ms}}^{-1}$
• B. $5{\text{ms}}^{-1}$
• C. $54{\text{ms}}^{-1}$
• D. $500{\text{ms}}^{-1}$

Answer 1

The correct option is C $54{\text{ms}}^{-1}$

Let $v$ be the velocity of the projectile after 5 sec.
Even after 5 seconds, the horizontal velocity $v_x$ will be $20{\text{ms}}^{-1}$ as there is no acceleration along horizontal direction.
The vertical velocity $v_y$ is given by
$v_y=u_y+gt$
(Take downward direction as positive)
$u_y=0$ ( $\because$ there is no initial velocity in the vertical direction)
$\Rightarrow v_y=0+10\times 5=50{\text{ms}}^{-1}$
So, speed after $5\text{sec}$
$v=\sqrt{v_x^2+v_y^2}=\sqrt{{20}^2+{50}^2}\approx 54{\text{ms}}^{-1}$