Question

The velocity vector of a particle moving in the xy plane is given by $\overrightarrow{v}=t\hat{i}+x\hat{j}$. If initially, the particle was at origin then the equation of trajectory of the projectile is?

Answer 1

We have, $\overrightarrow{v}=t\hat{i}+x\hat{j}$

We know, Equation of projectile is

$Y=X\tan \theta -\frac{g{X}^2(1+{\tan }^2\theta )}{2u^2}$

Here, $\tan \theta =\frac{x}{t}$

and $u=\sqrt{t^2+x^2}$

So, the required equation of trajectory of the projectile is

$Y=X\left(\frac{x}{t}\right)-\frac{g{X}^2(1+(\frac{x}{t}{)}^2)}{2(t^2+x^2)}$