The Skinny on Projectile Motion
The perpendicular components of motion (horizontal and vertical) are
independent of each other. Work them out separately.Horizontal (Range)
A projectile launched with horizontal velocity (v 0 x) maintains that
velocity. There are no accelerations in the horizontal force, so the x-
velocity is constant.Vertical (Time of Flight, Height)
The only vertical acceleration is 10 m/s^2 downward, so the vy
consistently decreases by this magnitude. At the top of the object’s
trajectory, vy = 0, and when the object reaches the same height from
which it was thrown, vy = −v 0 y.
The angle of launch determines the relationship of v 0 y and v 0 x.If θ > 45°, then v 0 y > v 0 x.If θ < 45°, then v 0 y < v 0 x.The quantity v 0 x, which is the horizontal (or x) component of the initial velocity, is
equal to v 0 cosθ 0 , where θ 0 is the launch angle, the angle that the initial velocity
vector, v 0 , makes with the horizontal. Similarly, the quantity v 0 y, the vertical (or y)
component of the initial velocity, is equal to v 0 sinθ 0.