Projectile Motion
2D Kinematics
When an object is launched with initial velocity and angle theta to the ground,
2 types of kinematics affect the motion of the object, the X-axis, and the Y-axis kinematics:
To calculate the velocity of the object in each of the two dimentions (axis) these formulas are used:
X-axis Velocity = Initial Velocity × cos(theta)
Y-axis Velocity = Initial Velocity × sin(theta)
Starting from here, the laws of kinematics can be used in both dimentions to calculate other quantities.
In the X-axis:
The velocity in the X-axis is constant, and the acceleration equals 0
Distance (s) = Vi × t
Vf = Vi
In the Y-axis:
The velocity in the Y-axis is variable, and the acceleration equals the gravitational potential
Distance (s) = Vi × t + 0.5 × a × t ^ 2
Vf = Vi + a × t
To calculate the time, maximum height, and range:
Time (t) = 2 × Vi × sin(theta) ÷ g;
Max Height (H) = Vi ^ 2 × sin(theta) ^ 2 ÷ 2 × g;
Range (R) = Vi ^ 2 × sin(2 × theta) ÷ g;