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) ?
Answer & explanation
Correct answer: option 4
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, \(KE \propto x^2 \Rightarrow \text{ parabola}\)
\(\text{For } x = 0, KE \neq 0\)