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

Step-by-step explanation:

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

`y=y_(o)+V_(oy)t-(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{(2 y_(o))/(g)}` (3)

`t=\sqrt{(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)