Achild's water pistol shoots water through a 1.0-mm-diameter hole. if the pistol is fired horizontally 70 cm above the ground, a squirt hits the ground 1.2 m away. what is the volume flow rate during the squirt? ignore air resistance.( in ml/s).

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:

where h = 0.7 m is the vertical distance, and t is the time it takes, which is what we are solving for:

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:

where s = 1.2 m is the horizontal distance

The cross-section area of the hole is

where r = d/2 = 0.001/2 = 0.0005 m is the radius of the hole

So we can calculate the volume flow rate:

or 2.52 ml/s

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