Answer:
[tex]v_{o}=8.85m/s[/tex]
Explanation:
To determine the muzzle velocity of the gun, we must know how long does it take the ball to strikes the ground
[tex]y=y_{o}+v_{oy}t+\frac{1}{2}gt^{2}[/tex]
Since the ground is at y=0 and [tex]v_{oy}=0[/tex]
[tex]0=1-\frac{1}{2}(9.8)t^{2}[/tex]
Solving for t
[tex]t=0.4517s[/tex]
Now, to determine the muzzle velocity we need to find its acceleration first
[tex]x=x_{o}+v_{ox}t+\frac{1}{2}at^{2}[/tex] (1)
[tex]v=v_{ox}+at[/tex] (2)
If we analyze the final velocity is 0. From (2) we have that
[tex]v_{ox}=-at[/tex] (3)
Replacing (3) in (1)
[tex]2=-at^{2}+\frac{1}{2}at^{2}[/tex]
[tex]2=a(0.4517)^{2} (\frac{1}{2}-1)[/tex]
[tex]a=-19.60m/s^{2}[/tex]
Solving (3)
[tex]v_{ox}=-at=-(19.60m/s^{2} )(0.4517s)=8.85m/s[/tex]
