Vectors AP Physics 1

What do you think? If vector B is added to vector A, under what conditions does the resultant vector A + B have the magnitude A + B? Under what condition is the resultant vector’s size equal to zero?

Speed 20 m/s Distance 20 m Time 15 s Scalar A Scalar is a quantity in physics that has magnitude but NOT direction Scalar Example Magnitude Speed 20 m/s Distance 20 m Time 15 s

Magnitude and Direction Vector A vector is a quantity in physics that has BOTH magnitude and direction. Vector Magnitude and Direction Velocity 20 m/s, N Acceleration 20 m/s/s, E Force 5 N, W Vectors are typically illustrated by drawing an arrow above the symbol or using boldface. The arrow is to convoy direction and magnitude. Notation A

Vector Addition Vector Addition - if two similar vectors point in the SAME direction, just add the magnitudes. Ex. #1 A man walks 54.5 m east, then another 30 m east. Calculate his displacement relative to where he started.

Answer 54.5 m E 30 m E 84.5 m E Notice that the size of the arrow is equal to the magnitude of the two vectors added and the way it was drawn points in the direction indicated in the problem.

Vector Subtraction If two vectors are going in the opposite directions, you subtract their magnitudes. Ex. # 2 A man walks 54.5 m east, then 30 m west. Calculate his displacement relative to where he started.

Answer 54.5 m E 30 m W 24.5 m E

Vector Addition – Graphical Method B Tail of the 1st to head of the last

Vector Addition: 2-D Component Method When two vectors are perpendicular, you can use the PYTHAGOREAN THEOREM. A2 + B2 = C2 Ex. # 3 A man walks 95 km east, then 55 km north. Calculate his resultant displacement.

Answer Vertical Component 55 km N The Hypotenuse in physics is called resultant Horizontal Component 95 km E A2 + B2 = C2 C = sq rt (A2 + B2 ) C = Resultant = 109.8 km N of E

Remember DIRECTION West of North East of North North of East North of West South of West South of East East of South West of South

Size of the angle? Note: Make sure your calculator is in degree mode! To find the value of the angle, we use TRIG function TANGENT. Tan ϴ - opposite side /adjacent side ϴ = Tan-1 (o/a)

What if you are missing a component? Ex. # 4 Suppose a man walked 65 m, 25 degrees East of North. What were is horizontal and vertical components. *** goal – make a right triangle

Answer 65 m ϴ = 25⁰ Cosine ϴ = Adjacent side/hypotenuse = {vertical component} Sine ϴ = opposite side/hypotenuse = {horizontal component} 58.91 m North 27.47 m East

Ex # 5 A bear, searching for food wanders 35 meters East then 20 meters North. Frustrated, he wanders another 12 meters west then 6 meters South. Calculate the bear’s displacement. 26.93 m, 31.3 degrees North of East

Ex. # 6 A boat moves with a velocity of 15 m/s North in a river which flows with a velocity of 8 m/s West. Calculate the boat’s resultant velocity with respect to due North. 17 m/s, 28.1 degrees West of North

Ex. # 7 A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane’s vertical and horizontal components. HC = 53.85 m/s E VC = 33.64 m/s S

Ex. # 8 A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm’s resultant displacement. 6224.14 km, 8.91 degrees North of East