Question

For a given angle of projection, if the initial velocity is doubled, the range of projectile becomes-

• A. Half
• B. One forth
• C. Two times
• D. Four times

Answer 1

The correct option is D Four times

The formula for range of a projectile is given by

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

Here, $u=$ initial velocity at projection
$\theta =$ angle of projection

From question, keeping $\theta$ constant (given)

$R\propto u^2$

$\therefore \frac{R_1}{R_2}={\left(\frac{u_1}{u_2}\right)}^2$

given that, $u_2=2u_1$

$\Rightarrow \frac{R_1}{R_2}={\left(\frac{u_1}{2u_1}\right)}^2=\frac{1}{4}$


$\Rightarrow R_2=4R_1$

Hence, option $\left(d\right)$ is correct.