Physics Calculator
Projectile Motion Calculator
Solve 2D kinematics and projectile motion problems effortlessly. Enter the initial velocity, launch angle, and launch height to calculate the maximum horizontal range, maximum altitude, time of flight, and visualize the trajectory using our interactive chart.
Projectile Motion Calculator
Calculate trajectory, range, and flight time
Results
Enter launch parameters and click Calculate
What is Projectile Motion?
Projectile motion refers to the motion of an object projected into the air and subject only to the acceleration of gravity. The object is called a projectile, and its path is called its trajectory.
In introductory physics, this motion is broken down into two independent one-dimensional motions: horizontal motion at constant velocity (since there is no horizontal acceleration if air resistance is ignored), and vertical motion undergoing constant acceleration due to gravity.
Kinematic Equations
This calculator uses the standard kinematic equations of motion. Here is how the key values are calculated:
Key Variables
- Initial Velocity (v₀): The speed at which the projectile is launched. Measured in meters per second (m/s).
- Launch Angle (θ): The angle relative to the horizontal. Measured in degrees. 45° yields the maximum range on flat ground.
- Initial Height (h₀): The starting elevation of the projectile. Measured in meters (m).
- Gravity (g): The acceleration due to gravity. Standard Earth gravity is 9.80665 m/s².
Frequently Asked Questions
- What is projectile motion?
- Projectile motion is a form of motion experienced by an object or particle that is projected near the Earth's surface and moves along a curved path under the action of gravity only (in particular, the effects of air resistance are assumed to be negligible).
- What assumptions does this calculator make?
- This calculator assumes ideal conditions: no air resistance (drag), constant acceleration due to gravity, a flat and non-rotating Earth. It is a perfect model for introductory physics problems.
- What is the optimal angle for maximum range?
- If the launch height and landing height are the same (h = 0), the maximum horizontal range is achieved at a launch angle of exactly 45 degrees. If the projectile is launched from an elevated position (h > 0), the optimal angle for maximum range is slightly less than 45 degrees.