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Learn about scalar and vector quantities, classification of vectors, solving for resultant vectors, displacement, and components of vectors. Explore examples and practice problems to master vector calculations.
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Scalar a quantity described by magnitudeonly examples include: time, length, speed, temperature, mass, energy Vector a quantity described bymagnitudeanddirection examples include: velocity, displacement, force, momentum, electric and magnetic fields
N 35 E of N E W 55 N of E 35 W of S S
N 58 E of N E W S
Classification of Vectors • Vectors at the same direction. • Vectors at opposite direction • Two or more vectors in different direction. • Forming a right triangle. • Vector at a certain angle.
Vector at the same direction. V2 = 20 blocks ↑ VR = 30 blocks ↑ V1 = 10 blocks ↑
Vector at different direction 10 m E 6m W VR = 4m E V1 = 25 m → VR = -15 m ← V2 = 40 m ←
Problem Set A Solve for the resultant vectors. Bobby walks 300 m East, stops to rest and then continues 400 m East. Janice walks home from school 300 m East and remembers that she has to bring home her Science book which a classmate borrowed. She walks back 500 m West to her classmate’s house.
To stay fit, Richard jogs around his neighborhood every morning. Calculate his total displacement from his house if he jogged 45 m to the East and 60 m to the West. Compute for the total distance a Komodo dragon has travelled if it walked 6 km Northward for 4 hours, took some rest for an hour or so, and walked 4 km in the same direction before sleeping.
Vectors with right triangle… Hypotenuse Opposite c2 = a2 + b2 Adjacent
Getting the Angle Sin = Soh Hypotenuse Opposite Cos = Cah Tan =Toa Adjacent
Example… • S.O.P • Illustrate the movement. • Identify the starting point and the end point. • Connect the head and tail with a broken line. • Identify your given (o, a or h) VR = 58 m 31 ° North of East V2 = 30 m N Θ ≈ 31° V1 = 50 m E
Problem Set After reading a book, Sarah stands up from the bench she was sitting on. She walks 600 m East, then turns 400 m North. What is her total displacement from the bench?
Problem Set Ann and Julie saw a bird outside Ann’s bedroom window. They saw that the bird moved 30 m North and 60 m West before it disappeared. What was the displacement of the bird from Ann’s window?
Problem Set A car is driven 125 km W then 65 km S. What is the magnitude of its resultant displacement? A shopper walks from the door of the mall to her car 250 m down the lane of cars, then turns 900 to the right and walks an additional 60 m. What is the magnitude of his resultant displacement of her car from the mall door?
Problem Set An ant crawls on a tabletop. It moves 2 cm East then turns 3.5 cm West. What is the ant’s total displacement? A boat leaves shore and travels 20 km North and then 15 km West. Find the boat’s resultant displacement vector.
Vector at an angle… Sin = Soh ? Cos = Cah ? Tan =Toa
Putting it in context… Opposite Sin (angle) (h) Vertical Component Perpendicular 45 N Adjacent Cos (angle) (h) Horizontal Component Parallel
Example…. 20 km/hr N 350 W E S
Try… • A golf ball hit from the tee travels 325 m in a direction 250 North of East. What are the East and North components of its displacement? • What are the components of a vector with a magnitude of 1.5 m at an angle of 300 to the positive x axis? • A hiker walks 14 km at an angle 360 south of east. Find the east and south component of this walk.
Food for thought… “You can’t change the direction of the WIND but you can always adjust your SAIL.”
Quick write • An airplane travels 600 m South then continue to travel 700 m West. Find its resultant displacement. • The wind is blowing at a velocity of 80 m/s at angle 350 above the horizontal. Find its vertical and horizontal components.
Three Vectors… A hiker walks 50 m E and turns right and walks 50 m S and finally walks 60 m E. What is the total displacement of the hiker?
