Question

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

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

Answer 1

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

$u=\sqrt{2^2+1^2}=\sqrt{5}$
$\theta =ta{n}^{-1}2$
$Equation:y=xtan\theta -\frac{g{x}^2}{2u^{2}co{s}^2\theta }$
$y=2x-\frac{10x^2}{2\times 5\times \frac{1}{5}}$
$y=2x-5x^2$