VECTORS

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

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

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

THE BOAT CURRENT DIRECTION OF BOAT

VECTORS AT RIGHT ANGLES Magnitude: Pythagorean Theorem a2 + b2 = c2 Direction: Tan Ѳ = opposite adjacent c b a

PYTHAGOREAN THEORM

Ex: A bird flew 4m east then 8m north relative to the ground Ex: A bird flew 4m east then 8m north relative to the ground. What is the displacement of the bird? a2 + b2 = c2 4m2 + 8m2 = c2 16 + 64 = c2 √80 =c C= 8.94m Tan Ѳ = 8m/4m Tan Ѳ = 2 Ѳ = Tan-1 2 Ѳ=63.4⁰ Ѳ C = 8.94m@63.4⁰ NE

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

Ex: A deer travels 10m east then turns 45⁰ and travels 15m NE Ex: A deer travels 10m east then turns 45⁰ and travels 15m NE. Find the deer’s displacement. c² = a² + b² − 2ab cos C c2 = 10m2 + 15m2-2(10)(15)cos 135 c2 = 100 + 225 – (-212) c2 = 537 c = 23m 45⁰ a = c 15m = 23m SinA SinC sinѲ Sin 135⁰ 23sinѲ = 15sin 135⁰ Ѳ = 27.5⁰ C = 23m @ 27.5 ⁰ NE

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

A car is displaced 300m at 30°NE from its starting position A car is displaced 300m 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 =300m cos30 Ax = 259.8m (Elm) Ay = AsinѲ Ay = 300m sin 30 Ay = 150m (Willow) 300m Willow Elm

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

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