A projectile is fired from ground level on a horizontal plain.If the initial speed of the projectile is now doubled,and we neglect air,
A)its range will be increased by $\sqrt { 2 }$
B)its range will double.
C)its range will be decreased by a factor of two.
D)its range will quadruple.
E)its range will decrease by a factor of four.

Question

Quizplus · Accepted Answer

The range of a projectile launched with initial speed $v$ at an angle $\theta$ to the horizontal is given by the formula $R = \frac{v^2}{g} \sin 2\theta$, where $g$ is the acceleration due to gravity. If the initial speed is doubled, the new range becomes $R' = \frac{(2v)^2}{g} \sin 2\theta = 4 \frac{v^2}{g} \sin 2\theta$, which is four times the original range. Hence, the range quadruples.

A Projectile Is Fired from Ground Level on a Horizontal 2\sqrt { 2 }2​

A Projectile Is Fired from Ground Level on a Horizontal $\sqrt { 2 }$