CLEAN POWER

Why does water fall in a parabolic arc when it spouts out from a hole in a bottle?

This is true of any free body acted on by gravity, be it a drop of water, a rock, or an artillery shell. This was first demonstrated by Galileo, and later verified by Newton.

You can calculate the vertical position y(t) of an object at any time, by using the equation:

y(t) = ½ g * t² + v(0) * t + y(0);

Where g is the acceleration due to gravity, v(0) is the initial velocity in the vertical direction, and y(0) is the initial position.

This equation naturally forms a parabola. Since I am guessing you are not familiar with calculus, I won’t confuse you with the details of how to derive this formula.

I will add a few caveats. First, this assumes that the acceleration of gravity is constant, which isn’t true if, for example, you are the space shuttle, or the moon.

Second, Air friction acts to resist the motion of any free moving object. In air, the above equation is only a good approximation for relatively dense objects. Strictly speaking, the motion of free projectiles in air, is a *hyperbola*, not a parabola. This becomes obvious if you shoot a stream of water 45 degrees into the air from a high pressure nozzle. The trailing end of the arc gets “clipped”, as air friction slows down the horizontal motion of the droplets.

This being the case, the *horizontal* position x(t) can be given by

x(t) = v(0)*t + C ln | t |;

where C is the coefficient of air resistance, and v(0) is the initial horizontal velocity.

I’m guessing thats more than you wanted to know,
~Soylent Yellow

the cooper temple clause – Zoology

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