Question

A body is projected with an initial velocity of $\left(\right.8\hat{i}+6\hat{j}\left.\right) \, m \, s^{- 1}$ . The horizontal range is ( $g=10 \, m \, s^{- 2}$ )

• A. $9.6 \, m$
• B. $14m$
• C. $50 \, m$
• D. $100 \, m$

Answer 1

Answer: (A)

velocity $= 8 \hat{i} + 6 \hat{j}$
$\left|\text{v}\right| = \text{10 m s}^{- 1}$
and angle $tan \text{\theta } = \frac{6}{8} = \frac{3}{4}$
Range $=\frac{u^{2} sin 2 \text{\theta }}{g}=\frac{u^{2} 2 sin \text{\theta } cos \text{\theta }}{g}$
$= \frac{\left(\text{10}\right)^{2} 2 \left(\frac{3}{5} \frac{4}{5}\right)}{\text{10}}$
$= \frac{\text{48}}{5} = \text{9.6} m$