Question

A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\text{m/s}$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10{\text{m/s}}^2$, the equation of its trajectory is :

• A. $y=x-5x^2$
• B. $4y=2x-5x^2$
• C. $4y=x-5x^2$
• D. $y=2x-5x^2$

Answer 1

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

From equation, $\overrightarrow{v}=\hat{i}+2\hat{j}$

$u_x=1\text{m/s};u_y=2\text{m/s}$

Now apply equation of motion along $x\&y$ axis,

$\begin{array}{}x=u_{x}t=1\times t=t& \text{(1)}\end{array}$
And,
$\begin{array}{}y=2t-\frac{1}{2}\left(10\right)t^2& \text{(2)}\end{array}$
From eqs. $\left(1\right)\&\left(2\right)$,

$y=2x-5x^2$

Therefore, option $\left(\text{D}\right)$ is correct.