T4.1c Vector Story Problems Please pick up the two sheets at the front.

3 1.ACT Review: What is the value of when x = 7 and y = -4 a.3375 b. 428 c. 225 d. 135 e In right triangle ABC, if C= 90°, A = 28°, and c = 42 in, find the length of side a. 3.Simplify: (No calculator on this one) A C B c = 42 in. 28° a = ? 19.7 = a

4 Active Learning Assignment?

5 LESSON: Equilibrant: the opposite of the resultant. It has the same magnitude, but 180° away. Resultant vector of A + B A’ B’ Equilibrant vector of A + B A B

6 Example 1: Find the magnitude of the equilibrant of forces 48 newtons and 60 newtons acting on a point, if the angle between them is 50°. Then find the angle between the equilibrant and the 48 newton force. Next, we need angle C. Why? 48 N 60 N C c 130° Since c = e, thus: The equilibrant is 98 newtons. e (Do you expect the resultant to be more or less than the component vectors?) First, draw it: Then use the Law of Cosines to find the resultant. 50 °

7 Find the magnitude of the equilibrant of forces 48 newtons and 60 newtons acting on a point, if the angle between them is 50°. Then find the angle between the equilibrant and the 48 newton force. We now have an angle and it’s opposite side, use the Law of Sines to find the angle between the 48 N force and the 98 N force. 48 N 60 N ? 50 ° 130 ° 98 N A = 28° Now, is that the answer? The angle between the 48 N and the equilibrant is 152°. A No, we need 180° – 28° = … *

8 Example 2: Two forces of 100 lbs and 150 lbs act on a point. The equilibrant is 200 lbs. Find the angle between the two vectors. This time we have SSS and need to find angle C. Why? 100 lbs 150 lbs 200 lbs C ? C = 104.5° The angle between the forces is 75.5°. We need 180° – 104.5° = … Draw it. (What do you suspect about the angle? Acute? Obtuse? Right? Why?) * Resultant But, is that the answer to the question?

9 Example 3: What is the force (one decimal place) required to pull a 50- lb weight up a ramp inclined at 20° to the horizontal? 50 lbs 20 Gravity pulls at 50 lbs This is the force required (x) 20 You can complete the triangle The force required is 17.1 lbs. Now, compare the forces required to: “pull up the incline” vs. “push up the incline” vs. “keep it in place”? Which takes the most force? Don’t answer out loud, but you must vote. x Ah, ha! Congruent triangles! Remember:

10 Example 4: What is the force, in pounds, (one decimal place) required to keep a 2-ton elephant on roller skates (at a stand-still) on a ramp at an incline of 25°? What do you notice about the units in this problem and what might you have to do, first? The force required is lbs. 25° 2 tons = 4000 pounds x 25 You can complete the triangle Gravity pulls at 50 lbs This is the force required (x)

11 As we close out the lesson, do you have any questions? As a group, please come up with a real-life situation involving vectors. It could be two forces acting on a point, or a gravity application that requires push, pull or maintaining. One recorder will write the answer on a single sheet and turn it in, with all your names on it. You may not have more than five minutes to do this, but as soon as you finish, you will begin the class assignment, on the next slide. When the bell rings, it will become a home assignment.

12 Active Learning Assignment: Vector II H/O #’s 1 – 7 Write the answers to the problems on your handout. Answers: 1) 93.9° 2) 70.1° 3) 18.2° 4) lbs. 5) 2.4 tons 6) 1618 lbs. 7) 2639 lbs., 167.2° with the 1480 lbs. force