Key Terms
SCALAR
Magnitude only. Speed, temperature, mass, distance.
Magnitude
A = sqrt(Ax^2 + Ay^2) Direction: theta = arctan(Ay / Ax)
To find A - B
The components of (-B) are the negatives of B's components. Rx = Ax - Bx Ry = Ay - By Then use steps 3 and 4 as normal.
Projectile
Object subject only to gravitational acceleration.
Trajectory
The path of a projectile.
Acceleration components
Ax = 0 (no horizontal force) ay = -9.8 m/s^2 (gravity, downward)
Horizontal (constant velocity)
X = v0x * t vx = v0x (constant; never changes)
Vertical (constant acceleration)
Y = v0y * t + (1/2) * ay * t^2 vy = v0y + ay * t vy^2 = v0y^2 + 2 * ay * y
EXAMPLE SETUP
Boat crossing a river
Direction relative to the bank
Theta = arctan(v_boat / v_river)
Analytical method
Using Pythagorean theorem and trig to find vector magnitude and direction; more precise than graphical methods.
Classical relativity
Study of relative velocities at speeds below 1% of the speed of light.
Commutative
Vector addition order does not matter; A + B = B + A.
Component
The piece of a vector along one axis (x or y).
Head-to-tail method
Graphical technique; place tail of each successive vector at the head of the previous one; draw resultant from first tai