Physics and New Year's Eve

Posted by Paul A. Heckert Jan 1, 2008

In some places, people fire shots into the air on New Year's eve and other celebratory occasions. This custom may seem harmless and even be relatively safe in sparsely populated areas. In densely populated areas, it can however be very dangerous. Physics tells us why.

First the obvious. From the law of gravity, whatever is fired into the air must come back down, unless it is fired fast enough to escape Earth's gravity and go into space.

Now a quick quiz. When the bullet returns to the ground, how fast is it moving? Is it slower than, faster than, or the same speed as when it left the pistol?

The bullet is propelled upward with its initial muzzle speed. Gravity tugs it downward, so it slows. At the highest point in its path it slows to a zero velocity for an instant. Gravity is still pulling it downward, so it begins its descent.

The gravitational force acting on the bullet remains constant the entire time, so the upward and downward speeds are reversed but symmetric. From this symmetry, when the bullet returns to the level it was fired from, its downward speed equals its initial upward speed. Air friction may slow the bullet a little, but no more than when it travels horizontally. If you picked the third choice, congratulations, you were correct.

If someone happens to be standing where the bullet comes back down, the results can be tragic. I have occasionally seen news stories about someone being accidentally shot this way.

There are safer ways to celebrate the new year and other occasions.

Have a good 2008.