Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be
A) two times that of Bill's ball.
B) roughly 1.4 times that of Bill's ball.
C) eight times that of Bill's ball.
D) four times that of Bill's ball.
E) equal to that of Bill's ball.

Question

Quizplus · Accepted Answer

The maximum height $h$ reached by an object thrown vertically is given by the formula $h = \frac{v^2}{2g}$, where $v$ is the initial speed and $g$ is the acceleration due to gravity. If Joe's initial speed is twice that of Bill's, substituting $2v$ for $v$ in the formula gives $h = \frac{(2v)^2}{2g} = \frac{4v^2}{2g} = 4 \times \frac{v^2}{2g}$, which is four times the height reached by Bill's ball.

Joe and Bill Throw Identical Balls Vertically Upward