Question

The velocity of projection of oblique projectile is $(6\hat{i}+8\hat{j})m{s}^{-1}$. The horizontal range of the projectile is

• A. $4.9m$
• B. $9.6m$
• C. $19.6m$
• D. $14m$

Answer 1

The correct option is B $9.6m$

$\overrightarrow{v}=6\hat{i}+8\hat{j}$
Comparing with $\overrightarrow{v}=v_x\hat{i}+v_y\hat{j}$ we get
$v_x=6m{s}^{-1}and{v}_y=8m{s}^{-1}$
also $v^2=v_x^2+v_y^2=36+64=100$
or $v=10m{s}^{-1}$

$\sin \theta =\frac{8}{10}$ and $\cos \theta =\frac{6}{10}$

$R=\frac{v^2\sin 2\theta }{g}=\frac{2v^2\sin \theta \cos \theta }{g}$

$R=2\times 10\times 10\times \frac{8}{10}\times \frac{6}{10}\times \frac{1}{10}=9.6m$