A projectile is projected with the velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$. The horizontal range of the projectile will be

• A

  $1.2 \mathrm{~m}$
• Correct answer
  B

  $2.4 \mathrm{~m}$
• C

  $3.6 \mathrm{~m}$
• D

  $4.5 \mathrm{~m}$

Solution

Given, $\mathbf{v}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}$ $$ \therefore \quad v=|\mathrm{v}|=\sqrt{3^2+4^2} \Rightarrow v=5 \mathrm{~m} / \mathrm{s} $$ From figure,
$\sin \theta=\frac{4}{5}$ and $\cos \theta=\frac{3}{5}$ $\because \quad R=\frac{v^2 \sin 2 \theta}{g}$ $=\frac{v^2 \cdot 2 \sin \theta \cdot \cos \theta}{g}$ $=\frac{5 \times 5 \times 2 \times \frac{4}{5} \times \frac{3}{5}}{10}=24 \mathrm{~m}$

Hence, the correct answer is option: 'B'.