What’s your vector, Victor?

Vectors and Scalars

A vector has magnitude as well as direction.

Some vector quantities: displacement, velocity, force, momentum

A scalar has only a magnitude.

Some scalar quantities: mass, time, temperature

3-2 Addition of Vectors – Graphical Methods

For vectors in one dimension, simple addition and subtraction are all that is needed.

You do need to be careful about the signs, as the figure indicates.

3-2 Addition of Vectors – Graphical MethodsIf the motion is in two dimensions, the situation is somewhat more complicated.

Here, the actual travel paths are at right angles to one another; we can find the displacement by

using the Pythagorean Theorem.

Headwind vs. Tail Wind

Vectors at right angles

How do we deal with a crosswind?(Add vectors head to tail)

Vector Addition

Vector Addition

• Connect each vector

• Add them “head to tail”

• Put the beginning of the second vector at the end of the first vector.

Vector Addition:Order doesn’t matter

Component Vectors

Component Vectors

Also see Sample Problem (p.73)

Component practice

• A ball is thrown with a velocity of 22.5 m/s at 30.0 degrees from east.

• What are the vertical (north/south) and horizontal velocity (east/west) components?

Solving for an angle

If vy is 12.4 m/s and vx is 15.4 m/s, find the angle θ

Warm up

• Find the resultant graphically for the following non right angled vectors.

• 10.5 m @ 32 NoW, 4.7 m @ 25 NoE

Finding ΔX and ΔY

• Steps to solve

1) Find the x value of each vector

2) Add the x values of each vector together (remember some vectors have negative x values)

3) Repeat steps 1 and 2 for the y component

Practice

• A unicyclist is riding through a city going due east for 250.0m. Then the unicyclist turns 120˚ counterclockwise and rides for 125.0m. Find Δx and Δy.

Practice

• An airplane takes off covering 7000.m in 20. sec at a 15˚angle. Then the airplane increases its angle of ascent to 35˚ for another 10.0 sec covering 3500 m. What is Δx and Δy for the 30 seconds?

Sketch then solve

After walking 11 km due north from camp, a hiker then walks 11 km due east.

a) What is the total distance walked by the hiker?

b) Determine the total displacement from the starting point and the direction

Sketch then solve

A motorboat heads across a lake due east for 859 m, then turns and travels 644 m, 57.0° E of N. What is the magnitude and direction of the resultant displacement?

Sketch then solve

Bob walks 115 m and then he walks 95 m. a)What is Bob’s displacement if he walks west both times

b)What is Bob’s displacement if he walks west then east?

c) What distance does Bob walk in each case

Sketch then solve

The direction to locate a buried time capsule tell you to walk 20.0 meters west from the front door of your school, turn 70.0 degrees to the north, and walk 20.0 more meters. Draw a sketch of the journey. Algebraically solve for Δx and Δy.

Sketch then solve

• Graphically, find the resultant velocity of the following two vectors:

• 92.3 m/s @ 73.0º W o N, 34.0 m/s @ 17.0º