Chapter 3 Projectile Motion Part 1 – Math Rev; intro to Trig and Vectors

Math Review or Introduction Right triangles and trig

What is a scalar quantity? Review… What is a scalar quantity? a quantity with magnitude Start with 8th

What is magnitude? How much of something you have; an amount only; a number

What is a vector quantity? A quantity that has both magnitude and direction

Right Triangles One side has a right angle (90°) The other two angles must add up to 90 Side opposite the right angle is the hypotenuse

Right Triangles con’t Pythagorean Theorem – know 2 sides; find third side

Examples 10 ? 15

Examples 35 17 ?

Examples 50 ? 100

Intro to Trig

Which side is the h, o and a?

3 Trig functions to find a side when given an angle NOTE: θ IS THE ANGLE IN DEGREES!

SOH CAH TOA (way to remember!)

Practice!!! 50° 7 ?

Practice!!! 30° ? 5

Practice!!! 50° ? 15

Practice 25 m 37° H = ?

Trig con’t (finding angles)

Finding the angle: use the inverse function Finding the angle: use the inverse function! (2nd key and then the function)

Practice Find angle A Find angle B

Find side X Find angle C

What a vector can represent: A drawn vector can be used to represent distance, velocity, acceleration or a force

Drawing Vectors… Length of the vector is the magnitude We use scaled drawings: like a map Angle and arrow indicate direction Direction can be in degrees, NSEW, both degrees and NSEW, up or down, left or right

Parts of a vector Tip – ending point (arrow) Tail – starting point

Drawing Vectors… degrees 90° 40° 180° 0° 360° 270°

Drawing Vectors… degrees 250°

Practice Drawing Vectors… 10 cm at 300 degrees 90° 180° 0° 360° 270°

Drawing Vectors… Degrees and N, S, E and W Example: 3 cm at 70° toward S from directly W (S of W) Put protractor on W and go 70° S 70°

Practice – draw a 6 cm vector at 40° towards North from directly E (N of E) Practice – draw a 4 cm vector at 60° towards E from directly S (E of S)

____° towards _____directly from ___________? How would you draw 340° ? How can we rename this angle to fit our standard form (note: angle between 0 and 90) ____° towards _____directly from ___________? START WITH 6TH ON NOV 13

Shortening the direction _____ of ____ Axis you start your measurement from…line up 0 degrees at this axis

Rewrite in shortened form…. draw a 5 cm vector at 30° towards North from directly E

Drawing Vectors… Example: 3 cm at 70° toward S from directly W Becomes 3 cm at ____________________________ 70°

Shortened direction? Practice – draw a 7 cm vector at 60° towards E from directly S

Adding Vectors Resultant the __________ of two or more vectors

2 main methods of adding vectors Head to tail method (aka tip to tail) Draw first vector Start next vector where the last one ended (so its tail is connected to the previous vectors tip)

Example: 2nd Vector 1st Vector

Drawing Resultant Start where the first vector starts and end where the last vector ends

Example: 2nd Vector Resultant 1st Vector

Practice Tip-to-Tail Method

Place the following quantities in the appropriate column…are they a scalar or vector quantity? Time Acceleration Distance Velocity Displacement Speed

2nd Method of adding vectors Tail-to-tail method: Also known as the Parallelogram Method Draw the first vector Draw the second vector starting from the tail of the first vector Start here with 3rd

Drawing the Resultant Form a parallelogram from the two vectors Do this by drawing lines that are parallel to the two vectors Resultant starts where the two vectors start and ends in the opposite corner

Example: Crosswind An airplane is flying 80 km/h north is caught in a strong crosswind of 60 km/h blowing from west to east. Will the airplane fly faster or slower than 80 km/h?

60 km/h 80 km/h 80 km/h Resultant 60 km/h

Then we can use the Pythagorean Theorem to find the hypotenuse which is our resultant A2 + B2 = C2 C = √(A2 + B2)

Graphically vs Mathematically adding vectors Graphically finding the information for vectors is using only a drawing and the measurements Mathematically is actually adding the numbers In most cases we will use both methods to double check our answers

Problems Involving Vectors

PE 1-6 Remember to set a scale! Be careful with directions! THINK through EACH problem Include magnitude and direction in your final answer

Vector Resolution or resolving the vector – Breaking the resultant vector into its two vector components HINT: you are given only ONE vector!

Parts of a vector: Vector Components Component – the two vectors at right angles with one another that are added to form the resultant (the single vector) (the x and y vectors aka the horizontal and vertical components)

To find the x and y: draw parallelogram around the resultant To find the x and y: draw parallelogram around the resultant! (graphically) Resultant

To find the x and y: mathematically Resultant