Fire a gun, drop a bullet from the same height. Which bullet hits the ground first?

Dear Cecil:

My high school physics teacher gave us this problem. Suppose you've got a bullet in one hand and a pistol in the other, aimed so it's perfectly level. You drop the bullet and fire the pistol at the same time.

Which bullet hits the ground first?

Cecil replies:

Dear Listener:

Get ready to take some notes, bud. Your physics teacher is going to regret the day he was ever born.

The average mope reasons like this. The dropped bullet falls only a few feet, whereas the fired bullet travels hundreds of yards. Ergo, the dropped bullet hits the ground first.

The average mope with a college education (e.g., a physics teacher) is a little more sophisticated.

He figures, hey, the force of the gun propels the fired bullet strictly horizontally. The only downward force is gravity, which acts equally on both bullets. Therefore they both hit the ground at the same time.

This is true. Up to a point. A BIG point. So much so that we must say that the only legitimate answer to this riddle is: it depends.

If the fired bullet travels only a short distance, then yes, both bullets hit the ground at the same time.

However, if the fired bullet travels far enough, the earth, being round, CURVES AWAY FROM IT. (Remember Newton’s first law of motion: moving objects tend to travel in a straight line.)

Since the fired bullet has farther to fall, it takes longer to hit the earth, so the dropped bullet hits the ground first.

What’s more, if the fired bullet travels fast enough (five miles per second, to be precise–a practical impossibility, but never mind), it reaches orbital velocity, goes into orbit around the earth, and NEVER HITS THE GROUND AT ALL.

Amazing, no? Try this one out in your next physics class. The teacher will go nuts, a huge argument will erupt, and you’ll kill the whole hour, guaranteed.

Send questions to Cecil via cecil@straightdope.com.

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