Question

A projectile is given an initial velocity of $\left(\hat{\text{i}}+2\hat{\text{j}}\right){\left(\text{m s}\right)}^{-1}$ , where $i$ is along the ground and $j$ is along vertically upward direction. If $g=10m{s}^{-2}$ , the equation of the trajectory is

• A. $y=x-5x^2$
• B. $y=2x-5x^2$
• C. $4y=2x-5x^2$
• D. $4y=2x-25x^2$

Answer 1

Answer: (B)

Initial velocity $=\vec{u}$
$\vec{u}=u_x\vec{i}$ & $u_y\vec{j}=\vec{i}+\overrightarrow{2j}$
Where $u_x=$ velocity along ground
$u_y=$ velocity along vertical direction
at time t, let $(x,y)$ be the coordinates of the projectile
$x=u_{x}t$ so $t=\frac{x}{u_x}$
But $u_x=1$ and $u_y=2$
$t=\frac{x}{1}=x$
$y=u_{y}t-\left(\frac{1}{2}g{t}^2\right)$
$y=2x-\left(\frac{1}{2}\right)\times 10x^2$
$y=2x-5x^2$ is the equation of the trajectory.