Vectors
How do you bring the horizontal and the vertical component together into a single resultant vector?
Pythagorean Theorem. V² = Vx² + Vy² The legs are the components. The hypotenuse is the resultant.
What is a *vector*?
Something that has both magnitude and direction.
What is a *scalar*?
Something that has only magnitude. (It does not have direction.)
How do you find the direction of a vector using its components?
Trigonometry (inverse tangent). θ = tan⁻¹ (Vy / Vx)
How do you break up a vector into components?
Trigonometry (sine and cosine).
formula for resultant vector from its components
V² = Vx² + Vy² (Pythagorean Theorem)
When using a vector formula, does the direction of the vectors matter?
YES. You can't mix horizontal and vertical components in the same vector formula.
formulas for horizontal and vertical components of a vector (assuming a normal, upright x-y axis)
horizontal component: Vx = Vcosθ vertical component: Vy = Vsinθ
Is *distance* a vector or a scalar?
scalar
Is *energy* a vector or a scalar?
scalar
Is *mass* a vector or a scalar?
scalar
Is *speed* a vector or a scalar?
scalar
Is *time* a vector or a scalar?
scalar
Is *work* a vector or a scalar?
scalar
Is *acceleration* a vector or a scalar?
vector
Is *displacement* a vector or a scalar?
vector
Is *field* a vector or a scalar?
vector
Is *force* a vector or a scalar?
vector
Is *velocity* a vector or a scalar?
vector
Is *weight* a vector or a scalar?
vector
formula for the direction of a vector from its components (angle with respect to the horizontal)
θ = tan⁻¹ (Vy / Vx)