You fire a gun and drop a bullet at the same time. Which bullet hits the ground first?

Dear Cecil:

My high school physics teacher gave us this problem once, but I forget what the answer was. 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:

You’ll excuse the physics, but this one is so twisted you gotta love it. 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. (We assume a vacuum throughout this discussion.)

Then we have the answer given by those who’ve achieved spiritual awareness as a result of regular reading of the Straight Dope. This may be summarized as follows: 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 (roughly five miles per second — a practical impossibility given atmospheric friction, but never mind), it goes into orbit around the earth and never hits the ground at all. Amazing, no? Try this one out in your next physics class and you’ll kill the whole hour, guaranteed.

Send questions to Cecil via cecil@straightdope.com.

Comment on this Column