A ball leaves the hand of a boy with a velocity v and travels a horizontal range R. In a second throw, the same ball leaves the boy's hand with a velocity of 2v. Compared to the first throw, the horizontal range is
A) the same.
B) two times larger.
C) half as large.
D) four times larger.
E) a fourth of the first.

Question

Quizplus · Accepted Answer

The horizontal range $R$ of a projectile is given by the formula $R = \frac{v^2 \sin 2\theta}{g}$, where $v$ is the velocity, $\theta$ is the angle of projection, and $g$ is the acceleration due to gravity. If the velocity is doubled, the range becomes $R' = \frac{(2v)^2 \sin 2\theta}{g} = 4\frac{v^2 \sin 2\theta}{g}$, which is four times the original range.

A Ball Leaves the Hand of a Boy with a Velocity