VECTORS PARALLEL VECTORS Make one value negative and

VECTORS

PARALLEL VECTORS Make one value negative and add together when they are in opposite directions.

ACCELERATION AND VELOCITY V A A V V A Accelerating to the right Decelerating to the right Accelerating to the left v A Decelerating to the left

RESULTANT VECTOR A resultant vector represents the sum of two or more vectors

THE BOAT CURRENT DIRECTION OF BOAT

VECTORS AT RIGHT ANGLES c a b Magnitude: Pythagorean Theorem a 2 + b 2 = c 2 Direction: Tan Ѳ = opposite adjacent

PYTHAGOREAN THEORM

• Ex: A bird flew 4 m east then 8 m north relative to the ground. What is the displacement of the bird? Tan Ѳ = 8 m/4 m a 2 + b 2 = c 2 4 m 2 + 8 m 2 = c 2 Ѳ 16 + 64 = √ 80 =c C= 8. 94 m c 2 Tan Ѳ = 2 Ѳ = Tan-1 2 Ѳ=63. 4⁰ C = 8. 94 m@63. 4⁰ NE

What about the other triangles? LAW OF COSINE: c² = a² + b² − 2 ab cos C LAW OF SINE:

Ex: A deer travels 10 m east then turns 45⁰ and travels 15 m NE. Find the deer’s displacement. c² = a² + b² − 2 ab cos C 45⁰ a = c Sin. A Sin. C c 2 = 10 m 2 + 15 m 2 -2(10)(15)cos 135 c 2 = 100 + 225 – (-212) c 2 = 537 c = 23 m 15 m = 23 m sinѲ Sin 135⁰ 23 sinѲ = 15 sin 135⁰ C = 23 m @ 27. 5 ⁰ NE Ѳ = 27. 5⁰

Vector Components • The two perpendicular vectors that combine to form the resultant. Ay A 30° Ax

Component formula’s X – component: Ax = A cos θ Y- component: Ay = A sinθ

m 300 Elm Willow • A car is displaced 300 m at 30°NE from its starting position. If it followed Elm street east and then turned north on Willow Street, how far did it travel on each street? Ax = AcosѲ Ax =300 m cos 30 Ax = 259. 8 m (Elm) Ay = AsinѲ Ay = 300 m sin 30 Ay = 150 m (Willow)

• As the angle of a resultant vector gets larger, The x component decreases The y component increases Y Y θ X

• At 45 degrees the x component is equal to the y component. Y 45° X