# If there is a cup filled with water and oil and I turn it upside down which one of this liquids will be first to hit the ground?

## Thanks

Jul 15, 2018

It depends on several things

#### Explanation:

Ignoring the affect of air resistance.

If the distance to the ground is short then the falling liquids will not get to a very high speed before they hit, so they will not be much affected by air resistance.

Both liquids are accelerated at the same rate regardless of their density.

In a vacuum they will continue to accelerate until they hit, regardless of distance.

If the cup is rotated quickly enough to allow both liquids to begin falling at the same moment then the one closest to the ground will hit first.
This will be the water as the inertia of the liquids will mean that they don't rotate with the cup.

If the cup is not turned upside down quickly enough then the oil will begin spilling (and falling) before the water has a chance to escape the cup.
$V = U + a t$
This means that once an object has an initial speed $\left(U\right)$, another object which is then dropped from stationary will never be traveling as fast as the first object ($a t$ is the same for both).
Once the oil is falling faster than the water, the water will never catch up (they will get further apart as time increases) .

With air resistance.

Air resistance can make the result harder to predict.

If the liquids are falling through air far enough then as they move faster and faster they will be more and more affected by air resistance.

This will result in a force in the opposite direction to that in which they are traveling (assuming no wind). They will eventually reach terminal velocity.

The air resistance is not independent from density. Terminal velocity is different for different densities and shapes.
As a rule, denser more compact objects have higher terminal velocity.

Liquids tend to break up into individual blobs or droplets, which are even more affected by air.