How to Calculate the Distance of a Projectile

How can you calculate where a thrown football would land?

You can easily calculate the horizontal distance that a projectile will travel if you know the right equation to use. The distance of a projectile is dependent upon three critical factors: its initial velocity, the angle at which it was launched, and the acceleration due to gravity. Initial velocity and gravity are important because the faster the projectile travels, the farther it will go before gravity pulls it back to Earth. The launch angle determines how much the projectile will travel vertically versus horizontally. These three factors can be combined into one equation to calculate the distance of a projectile.

Things You'll Need

• Calculator

Instructions

1. Write the equation for the horizontal range of a projectile:

   Range = (V^2 x sine (2 x A)) / g, where

   V = initial velocity
   ^ = symbol that means "to the power of"
   A = launch angle
   g = acceleration due to gravity = 9.8 meters per square second (m/s^2)

2. Consider the parameters of the projectile for which you are calculating the range. For example, suppose that a football is thrown at a 30 degree angle from the ground with an initial velocity of 20 m/s.

3. Plug your values into the equation and use a calculator to work out the distance the projectile would travel. In the football example, the calculation would look like this:

   Range = (20^2 x sine (2 x 30)) / 9.8 = 35.3 m

   The football would land 35.3 meters from where it was thrown.

References

• Georgia State University: Projectile Motion