Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw their javelin in such a way that it travels as far as possible. The javelin thrower takes a short run-up to increase the initial speed of the javelin. The range of a projectile is at its maximum at a 45° angle so javelin throwers try to angle their throw as close to 45° as possible.

When we speak of the range (R) of a projectile on level ground, we assume R is very small compared with the circumference of the Earth. If, however, the range is large, the Earth curves away below the projectile, and the acceleration resulting from gravity changes direction along the path. The range is larger than predicted by the range equation given for level ground because the projectile has farther to fall.

If the initial speed is large enough, the projectile goes into orbit. The Earth's surface drops 5 m every 8000 m. In 1 s, an object falls 5 m without air resistance. Thus, if an object has a horizontal velocity of 8000 m/s near the Earth's surface, it will go into orbit around the planet because the surface continuously falls away from the object. This is roughly the speed of a space shuttle in a low Earth orbit (when they were operational) or any satellite in a low Earth orbit.

This text is adapted from Openstax, University Physics Volume 1, Section 4.3: Projectile Motion.