Vector Test Review
Learning Goals:
 I can draw vectors using the tip-to-tail method and label the vectors properly
 I can solve 2D problems using vector addition, vector subtraction and vector component
methods
 I can apply math skills such as Pythagorean theorem, trig ratios, cosine and sine laws, and
components
1.
2.
3.
4.
5.
Concepts:
Vector Addition
 Used to solve displacement problems in 1D and 2D where
∆𝑑 𝑇 = ∆𝑑1 + ∆𝑑2 + ⋯ + ∆𝑑𝑛
 In 1D solve by simply adding vectors tip-to-tail *watch directions
 In 2D draw vectors tip-to-tail and then solve using one of the following methods:
1) Pythagorean Theorem and trig ratios if 90° triangle
2) Cosine/sine law if non-90° triangle
3) Components for any type of problem
 If asked to calculate avg. velocity, first solve for ∆𝑑 𝑇 , then solve for avg. velocity using:
∆𝑑
𝑣𝐴𝑉 = ∆𝑡
 If asked to calculate ∆𝑑𝑇 but are given velocities and time, first calculate ∆𝑑1 = 𝑣1 × ∆𝑡
and ∆𝑑2 = 𝑣2 × ∆𝑡, then solve for ∆𝑑 𝑇 using
∆𝑑 𝑇 = ∆𝑑1 + ∆𝑑2 in 2D
Vector Subtraction
 Used to calculate a change in velocity in 2D: ∆𝑣 = 𝑣2 − 𝑣1
 *Always reverse the direction of 𝑣1 , then solve using 1 of 3 methods listed above
 To calculate acceleration, first calculate ∆𝑣 = 𝑣2 − 𝑣1 then solve for acceleration using
∆𝑣
𝑎 = ∆𝑡
Vector Components
 Used to calculate any quantity
 *Angles are measured either from positive x-axis or using complimentary angle with xaxis and assigning direction of component as +/Relative Velocities and Vectors
 Relative velocities describe motion with respect to a specific coordinate system
 May solve problems using any of 3 methods listed above
 ***Watch subscripts and Chain Rule
General
 Read problems carefully
 Write down all information given
 DRAW DIAGRAMS!!!! You must include subscripts if relative velocities
 Watch sig.digs. and units
Suggested Review Problems:
Ch.3 Review pg. 129 #4, 9, 11, 13-20, 22-26 (answers in back of book)
pg. 103 #1ab, 2, 3, 5; pg.113 #2, 3, 4, 7, 8; pg.128 #3-7