Kinematics Reasonings

If the initial velocity of a projectile is doubled, what happens to its maximum range?

OR: What would be the effect on the maximum range in doubling the velocity of a projectile?

Let a body be projected with velocity $u$ by making an angle $\theta$ with horizontal. If $R$ is the horizontal range of the projectile, then \[R=\frac{u^2\sin2\theta}{g}\]

If the velocity of firing is doubled, $u’=2u.$ Then, the new range will be \[R’=\frac{u’^2\sin2\theta}{g}=\frac{4u^2\sin2\theta}{g}=4R\]

So, the new range will be four times the original.

[Read: Projectile Motion]