In order to do an analysis of the motion of a projectile, it demands that the two components of motion are analyzed independent of each other, being careful not to mix horizontal motion information with vertical motion information. That is, if analyzing the motion to determine the vertical displacement, one would use kinematic equations with vertical motion parameters (initial vertical velocity, final vertical velocity, vertical acceleration) and not horizontal motion parameters (initial horizontal velocity, final horizontal velocity, horizontal acceleration). It is for this reason that one of the initial steps of a projectile motion problem is to determine the components of the initial velocity.

Understanding Vector Components

Vector components are needed when calculating vector resolution. Vector resolution is the method of taking a single vector at an angle and separating it into two perpendicular parts, horizontal and vertical. The two parts of a vector are known as components and describe the influence of that vector in a single direction. If a projectile is launched at an angle to the horizontal, then the initial velocity of the projectile has both a horizontal and a vertical component. The horizontal velocity component (v_x) describes the influence of the velocity in displacing the projectile horizontally. The vertical velocity component (v_y) describes the influence of the velocity in displacing the projectile vertically. This is where we need to understand some trig! Take a look:

Problem 2

A water balloon is launched with a speed of 40 m/s at an angle of 60 degrees to the horizontal.

(ans: Vx=20.0 m/s, Vy=34.6 m/s)

Problem 3

A motorcycle stunt person traveling 70 mi/hr jumps off a ramp at an angle of 35 degrees to the horizontal.

(ans: Vx=57.3 mph, Vy=40.1 mph)

Problem 4

A springboard diver jumps with a velocity of 10 m/s at an angle of 80 degrees to the horizontal.

(ans: Vx=1.7 m/s, Vy=9.8 m/s)