Answer:
2.52 ml/s
Explanation:
Unit conversions:
1 mm = 0.001m
70 cm = 0.7 m
Let g = 10m/s2. If the pistol is fired horizontally at first, it did not have an vertical velocity, only horizontal velocity. So g is the only thing that affects the vertical motion of water.
We can calculate the time it takes for the squirts to hit the ground in the following equation of motion:
[tex]h = gt^2/2[/tex]
where h = 0.7 m is the vertical distance, and t is the time it takes, which is what we are solving for:
[tex]t^2 = 2h/g = 2*0.7/10 = 0.14[/tex]
[tex]t = \sqrt{0.14} = 0.374 s[/tex]
So the squirts takes 0.374s to hit the ground, and within that time it travels a distance of 1.m horizontally. Neglect air resistance, we can calculate the horizontal velocity:
[tex]v = s/t[/tex]
where s = 1.2 m is the horizontal distance
[tex]v = 1.2/0.374 = 3.21 m/s[/tex]
The cross-section area of the hole is
[tex]A = \pi r^2[/tex]
where r = d/2 = 0.001/2 = 0.0005 m is the radius of the hole
[tex]A = 0.0005^2 \pi = 7.85*10^{-7}[/tex]
So we can calculate the volume flow rate:
[tex]\dot{V} = v*A = 3.21*7.85*10^{-7} = 2.52 * 10^{-06} m^3/s[/tex]
or 2.52 ml/s
