Table of Contents
What Is Projectile Motion?
Projectile motion describes the motion of an object launched into the air that moves under the influence of gravity alone, following a parabolic trajectory. This type of motion combines horizontal motion at constant velocity with vertical motion under constant gravitational acceleration.
The analysis assumes no air resistance and a uniform gravitational field. While these assumptions are idealizations, they provide an excellent approximation for many practical situations, such as throwing a ball, launching a cannonball, or analyzing sports trajectories over short distances.
Key Formulas
For launch from an elevated position h0, the time of flight is found by solving: h0 + vyt - (1/2)gt² = 0 using the quadratic formula, and the range is R = vx × T.
Example Calculations
| Scenario | v (m/s) | Angle | Range (m) | Max Height (m) |
|---|---|---|---|---|
| Baseball throw | 40 | 35° | 156.5 | 26.8 |
| Soccer kick | 30 | 45° | 91.7 | 22.9 |
| Golf drive | 70 | 12° | 205.1 | 10.7 |
| Cannon shot | 200 | 30° | 3531 | 510 |
Frequently Asked Questions
What angle gives the maximum range?
For launch from ground level, 45 degrees gives the maximum range. If launching from an elevated position, the optimal angle is slightly less than 45 degrees because the projectile has extra time to travel horizontally during its descent.
How does air resistance affect projectile motion?
Air resistance reduces both range and maximum height. The actual trajectory is asymmetric: the descent is steeper than the ascent, and the maximum range angle drops below 45 degrees. For fast projectiles, drag can reduce range by 50% or more.
Does mass affect projectile trajectory?
In vacuum (no air resistance), mass has no effect on trajectory. All objects follow the same path regardless of mass. In air, heavier objects are less affected by drag (they have higher ballistic coefficients), so they travel farther than lighter objects of the same shape and size.