Question

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\text{m/s}$. The cartesian equation of its path is $(g=10{\text{m/s}}^2)$

• A. $y=2x-5x^2$
• B. $y=x-5x^2$
• C. $y=2x-1.25x^2$
• D. $y=2x-25x^2$

Answer 1

The correct option is A $y=2x-5x^2$

We have, $\overrightarrow{u}=\hat{i}+\hat{2}j$
Comparing with $\overrightarrow{u}=u_x\hat{i}+u_y\hat{j}$, we have
$u_x=1,u_y=2$
and $\tan \theta =\frac{u_y}{u_x}=2$
Now, $u_x=u\cos \theta$,

Thus, the equation of the path of projectile is given by
$y=x\tan \theta -\frac{g{x}^2}{2u^2{\cos }^2\theta }$
$y=x\tan \theta -\frac{g{x}^2}{2(u_x{)}^2}$
$y=x\times 2-\frac{10x^2}{2}$
$y=2x-5x^2$
Option A is correct.