1. 8.5.4 – Magnitude and Angles

2. We have already discussed finding the magnitude of vectors in various forms Especially, in component form But, sometimes we may have to go the other way around – Given a magnitude, find the components

3. Magnitude/Angle In order to find separate components using the magnitude, we need other information Specifically, the angle will help us

4. So, from the picture, we can derive; u = {||u||cosϴ, ||u||sinϴ} = ||u||{cosϴ, sinϴ} – The angle ϴ is the same as we have used before; angle with respect to the x-axis

5. Sometimes, we will be able to discern the angle and magnitude just by looking at a particular equation Other times, we may need to form a triangle using information about the vector, and use trig to help us – Recall your basic trig functions – SOH-CAH-TOA

6. Example. Find the magnitude and direction angle of the vector v. v = 10(cos(60)i + sin(60)j) v = 4(cos(pi)i + sin(pi)j)

7. Example. Find the magnitude and direction angle of the vector v. v = 3i + 4j – What is this vector in component form?

8. Example. Find the magnitude and direction angle of the vector v. v = i – 3j – What is this vector in component form?

9. Finding Component Form When given a magnitude and direction angle theta, we simply need to use the formula u = {||u||cosϴ, ||u||sinϴ} Example. Find the component form of v given ||v|| = 2, ϴ = 120 degrees

10. Example. Find the component form of v given ||v|| = 1, ϴ = 45 degrees

11. Word Problems To perform word problems, we must be able to determine what represents a magnitude, and do our best with particular angles – Speed = magnitude Remember, velocity is a vector with a magnitude (speed) and direction (theta)

12. Example. A baseball is hit by a bat at a speed of 8.2ft/sec and at an angle of 34 degrees from the horizontal. Express the velocity in vector form.

13. Example. A cat is pushing a 5 pound plant across a table. The cat is pushing the pot with a force of 2 pounds. What is the total force? Total Force = F(1) + F(2) [total of aggregate forces] Consider which way the forces are being applied

14. Assignment Pg. 668 33-36 all 38-44 even 45, 46, 49, 50