Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\overrightarrow{u}$ = ($\hat{i}$+2$\hat{j}$) $m{s}^{-1}$ $\Rightarrow$ $u_x$ = 1, $v_y$ = 2

$\Rightarrow$ tan$\theta$ = $\frac{v_y}{u_x}$ = 2

Range, R = $\frac{2u_x{v}_y}{g}$ = $\frac{2\left(1\right)\left(2\right)}{10}$ = $\frac{2}{5}$ m

Trajectory,

y = x tan$\theta$[1 - $\frac{x}{R}$]

y = 2x[1 - $\frac{5x}{2}$]

y = 2x - 5$x^2$