Question

A ball is horizontally projected off the end of a bench 1.25m above the ground with a speed of 4m/s .How far from the base of the bench does the ball land?

Answer 1

Answer: 2 m

Explanation:

We can solve this problem related to parabolic motion with the following equations:

$y=y_{o}+V_{oy}t-\frac{1}{2}gt^{2}$ (1)

$x=V_{ox}t$ (2)

Where:

$y=0 m$ is the ball's final jeight

$y_{o}=1.25 m$ is the ball's initial height

$V_{oy}=0 m/s$ is the ball's initial vertical velocity, since the ball is horizontally  projected

$t$ is the time

$g=9.8 m/s^{2}$ is the acceleration due gravity

$x$ is the ball's horizontal range

$V_{ox}=4m/s$ is the ball's initial horizontal velocity

Isolating $t$ from (1):

$t=\sqrt{\frac{2 y_{o}}{g}}$ (3)

$t=\sqrt{\frac{2 (1.25 m)}{9.8 m/s^{2}}}$ (4)

$t=0.5 s$ (5)

Substituting (5) in (2):

$x=(4 m/s)(0.5 s)$ (6)

Finally we find how far horizontally the ball lands:

$x=2 m$ (7)