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)