Trajectory

Definition

A trajectory is the path that a projectile follows through space as a function of time. It is determined by initial velocity, launch angle, and the forces acting on the projectile, such as gravity and air resistance.

5 Must Know Facts For Your Next Test

1. The shape of a projectile's trajectory under the influence of gravity alone is a parabola.
2. The horizontal component of velocity remains constant if air resistance is neglected.
3. The vertical component of velocity changes linearly with time due to gravity, following $v_y = v_{0y} - gt$.
4. The maximum height of the trajectory can be calculated using $h_{max} = \frac{v_{0y}^2}{2g}$.
5. The range of a projectile (the horizontal distance traveled) can be found using $R = \frac{v_0^2 \sin(2\theta)}{g}$ where $\theta$ is the launch angle.

Review Questions

• What shape does the trajectory of a projectile take under uniform gravitational force?
• How does the horizontal component of a projectile's velocity change in the absence of air resistance?
• What equation would you use to calculate the range of a projectile launched at an angle?

Related terms

Initial Velocity:

The speed and direction at which an object is launched or begins its motion.

Launch Angle: The angle at which an object is projected relative to the horizontal axis.

Gravity:

A force that attracts any two objects with mass towards each other, commonly approximated as $9.8 \, m/s^2$ on Earth's surface.