Question

A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the total kinetic energy of a projectile $\left(\text{KE}\right)$ versus its horizontal displacement $\left(x\right)$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Let the projectile fired with velocity $u$ at angle $\theta$ with horizontal.

Initial kinetic energy $=\frac{1}{2}m{u}^2$
We know $u_x=u\cos \theta$ will remain contant for entire motion as acceleration along $x-$ axis is zero.
But Velocity along $y-$ axis $\left(v_y\right)$ will change due to gravity.
$\because a_y=g{\text{m/s}}^2$
$\therefore \text{KE}$ at any instant $=\frac{1}{2}m(\sqrt{u_x^2+v_y^2}{)}^2$
$=\frac{1}{2}m(u_x^2+v_y^2)$

At maximum height $v_y=0$, before that velocity is continuously decreasing and after that continuously increasing.
Thus, $\text{KE}$ first decreases and then increases.