A projectile is fired with some velocity making certain angle with the horizontal. Which of the following graphs is the best representation for the kinetic energy of a projectile (KE) versus its horizontal displacement (x) ?

Velocity of a projectile at any instant of time (t) : v 

\(v^2 = v^2_x + v^2_y\)

    \(=(u \cos {\theta})^2 + (u \sin {\theta} - g\frac{x}{u \cos {\theta}})^2\)

\(\Rightarrow KE = \frac{1}{2}mu^2 - mgx \tan {\theta} + \frac{mg^2 x^2}{u^2 \cos^2 {\theta}}\)

Thus, \(KE \propto x^2 \Rightarrow \text{ parabola}\)

\(\text{For } x = 0, KE \neq 0\)