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Q & A: Shooting and dropping bullets

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If you shot a bullet parallel to the Earth’s surface and dropped a bullet at the same time from the same height, would both bullets hit the ground at the same time?
- David
Clear Lake High School, Texas
Well, the simplified physics textbook problem would probably want the answer "yes," since you can treat Newton's second law and the resulting kinematics of uniformly accelerated motion separately for the horizontal and vertical components of the motion. They probably tell you to treat the air resistance as being zero and treat the Earth as flat, both of which we know not to be true.

But more realistically, air resistance provides a drag force which increases with speed and points in the direction opposite to the velocity of the bullet through the air. The bullet is traveling very rapidly, mostly horizontally, but with a small downwards component. Air resistance provides a force that increases nonlinearly with speed, and so the vertical component of the air resistance force will be greater for the horizontally shot bullet than for the dropped bullet.

If the bullet is shot very fast, the curvature of the Earth becomes important (say if this is an artillery shell being shot at a target many miles away). Shoot a bullet fast enough in the horizontal direction, ignore air resistance, and you can get it in orbit around the Earth.

Alternatively, if there's a hill nearby, you could get the opposite answer.

Tom J.

(republished on 07/12/06)

Follow-Up #1: Falling bullets

So what is the answer to the question??

Which bullet will hit the earth first?? Iíve been arguing this with a mate for years. I think the one dropped will hit the earth before the bullet that is shot.

write back to (deleted)
- Dombowski (age 27)
Hong Kong
Before one can answer a yes/no, black/white kind of question that you have posed you must be extremely precise in specifying all the environmental conditions involved.  Do you want to neglect air resistance, air currents, the earthís rotation,  geographical position, direction of firing, and on and on and on...?    The classic high school text answer is that they both fall to the earth at the same time.  However if you are at the earthís equator the answer depends on whether you are firing toward the east or toward the west.  Figure that one out... you can have more arguments with your mate.


(published on 08/21/07)

Follow-up on this answer.