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Please get a calculator today.  4-4-17 T4.1b Vectors: I) Find the Horizontal & Vertical Components; II) Find the Resultant of Two Forces Acting on a Point Please get a calculator today. 

OPENER: Given the following vectors, find: (use the Parallelogram Rule on # 3 & #4) b a a 1) -a 2) - b -a 2b a’ b’ 4) a – b b b 3) a + b a –b’ a + (– b) b a + b –b a a – b a’

Active Learning Assignment?

#1 #2 #3 LESSON: I) Find the Horizontal & Vertical Components We know how to get the resultant from two components, but, how do we get the components from a resultant? (Poor orphaned resultant) “It takes a village to raise a child…” Which would make the best parents and why? #1 #2 #3 “Because they were right for each other” -Michael French, Class of 2012

The horizontal is 8.6 units and the vertical is 12.3 units. Ex: Given α = 55° (the direction) and |v| = 15 (the magnitude), find the magnitude of the horizontal and vertical components. ( 1 dec. pl.) y x 15 55 ? hyp. opp. (y) ? adj. (x) The horizontal is 8.6 units and the vertical is 12.3 units. * * * Formulas? *Can say “x value” or “y value” instead

The horizontal is 45.8 units and the vertical is 41.8 units. Try: Given α = 137°40´ and |v| = 62, find the magnitude of the horizontal and vertical components. ( 1 dec. pl.) y 62 Remember to put cos(137°40’) in the calculator as cos(137 + 40/60) | y | 137°40´ x | x | The horizontal is 45.8 units and the vertical is 41.8 units.

* The resultant force is 24.4 newtons. This is Olivia Newton John. II) Find the Resultant of Two Forces Acting on a Point Ex: Two forces of 15 newtons and 22 newtons act on a point and the angle between them is 100° . Find the magnitude of the resultant force. ( 1 dec. pl.) What other pieces of information can we find? Two things: the resultant does NOT cut the angle in half, and it does not create a right triangle!!! 15 n 22 n 180° – 100° = 80° WHY? 15 n 22 n 100° 80° ? We can now use the Law of Cosines, SAS. * The resultant force is 24.4 newtons. This is Olivia Newton John.

The resultant is 50.3 newtons. Try: Two forces of 25 newtons and 31 newtons act on a point and the angle between them is 52° 40´. Find the magnitude of the resultant force. ( 1 dec. pl.) Remember to subtract 52°40’ from 180°, use 179°60’ – 52°40’ 25 n 31 n 25 n 31 n 52° 40´. 127° 20´. The resultant is 50.3 newtons.

Active Learning Assignment: Vector I Handout 30-46 evens Answers are in horizontal (x), then vertical (y). Write answers 47, 17 38. 198, 132 46. 76.2 lbs. 51, 141 40. 4259, 6642 34. 38.8, 28.0 42. 29 N 39.8, 68.1 44. 131 lbs.