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 $g=10 \, m \, s^{- 2}$ , 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 } $ & $u _{ y } \vec{ j }=\vec{ i }+\vec{2 j }$
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 $u_y=2$
$t=\frac{x}{1}=x$
$y=u_y t-\left(\frac{1}{2} g t^2\right)$
$y=2 x-\left(\frac{1}{2}\right) \times 10 x^2$
$y=2 x-5 x^2$ is the equation of the trajectory.