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How to Calculate a Bullet's Drop

What goes up must come down. Put another way, whatever isn't held up, drops. After a bullet leaves a barrel, nothing is holding it up, so it falls. It doesn't matter if the bullet is dropped or it is fired horizontally, it hits the ground at the same time. Of course, it will be in a different place.

Instructions

- 1
  Calculate the acceleration due to gravity. You will find it is 9.8 meters per second squared. That means that each second an object falls, it will have a downward speed 9.8 meters per second faster than the previous second.
- 2
  Insert the height of the rifle barrel into the equation of motion for an object in free fall. The position of a dropped object is given by the expression vertical position = initial height - (1/2) x g x t^2, where g is the acceleration of gravity. The time for the object to hit the ground, where the vertical position is zero, is given by t = sqrt (2 x initial height/g). So, if an object is dropped from a height of 1.5 meters, it will hit the ground at t = sqrt (3 / 9.8) = 0.55 seconds.
- 3
  Calculate the horizontal motion of the bullet. Assume a muzzle velocity for the rifle -- a reasonable rifle velocity is something like 750 meters per second -- and assume air resistance is negligible, which means there is no acceleration in the horizontal direction. The equation of motion for a situation with no acceleration is position = v x t. Specifically, for this rifle bullet, the horizontal position is 750 meters per second x time.
- 4
  Calculate the position of the bullet at the time when it hits the ground. The time it hits the ground is given as the value t. Insert that time in the equation ffor horizontal motion. The bullet will hit the ground at the horizontal position given by v x sqrt (2 x initial height/g) = 750 x sqrt (3 / 9.8) = 412.5 meters away. It will hit at exactly the same time as if it were dropped, but it will be about 413 meters away.

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