**Vectors and Scalars**

**Vectors and Scalars**

__Reading__

BJU book: Ch. 4 "Vectors and Scalars"

__Topics__

Working with vectors

Solving right triangle problems with sine, cosine, and tangent

__Lecture outline:__

Be able to use "SOH-CAH-TOA" to solve problems

- Sine = opposite/hypotenuse
- Cosine = adjacent/hypotenuse
- Tangent = opposite/adjacent

To solve these problems and determine the resultant vector 'R', follow this sequence:

- Draw a nice, big sketch
- Resolve the individual vectors (typically 2 or 3) into their 'x' and 'y' components
- Then, to solve for the 'x' and 'y' components of the resultant vector, add the 'x' and 'y' components of the individual vectors together. BE CAREFUL OF SIGNAGE HERE.
- Determine the angle of the resultant vector 'R' using SOH-CAH-TOA
- Determine the magnitude of the resultant vector 'R' using the Pythagorean theorem.

Know the difference between Scalars and Vectors

- A scalar quantity has "magnitude" only. Examples: 1) an airplane flies at 50 m/s... 2) a man walks at 1.5 m/s.
- A vector has magnitude AND direction. Examples: 1) an airplane flies due north at 50 m/s... 2) a naval gun fires at a horizontal angle of 20 degrees and a muzzle velocity of 800 m/s.

__Lab__

Outdoor surveying lab: Vectors

We will use commercial surveying equipment (transit-level) to determine the distance of a far-away object (more than 1 mile away) using nothing but angles and vector measurements.

Then we will compare our calculated distance with Google Earth to see how close we came.

If we do this carefully, you may be surprised at how close we come to the 'actual' distance.

__Lab Extension assignment__

3._surveying_for_a_new_bridge__vectors_lab_extension_.pdf |

__Homework__