Question

What is a projectile? Derive an equation of the path of a projectile

Answer 1

When a body is thrown with velocity making some angle with horizontal,it follows parabolic trajectory called projectile.

At general time ,velocity of the particle will be $v\cos \theta \hat{i}+(v\sin \theta -gt)\hat{j}$

$v_x=v\cos \theta$

$v_y=(v\sin \theta -gt)$

$X=v\cos \theta t$

$Y=v\sin \theta t-\frac{g{t}^2}{2}$

Eliminating t,$Y=\frac{v\sin \theta x}{v\cos \theta }-\frac{g\times x^2}{2v^2{\cos }^2\theta }$

$Y=x\tan \theta -\frac{g\times x^2}{2u^2{\cos }^2\theta }$ is called equation of trajectory.