UNIT 2 Two Dimensional Motion And Vectors

ConcepTest 3.1a Vectors I 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B?

ConcepTest 3.1a Vectors I 1) same magnitude, but can be in any direction 2) same magnitude, but must be in the same direction 3) different magnitudes, but must be in the same direction 4) same magnitude, but must be in opposite directions 5) different magnitudes, but must be in opposite directions If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B? The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sum to come out to zero. You can prove this with the tip-to-tail method.

Monday September 19th Introduction of Vectors

TODAY’S AGENDA UPCOMING… Intro to Vectors Monday, September 19 Intro to Vectors Mini-Lesson: Properties of Vectors Hw: Worksheet Pg. 13-14 UPCOMING… Tues: Vector Operations Wed: More Vector Operations Thurs: Problem Quiz 1 Vectors Mini-Lesson: Projectile Motion

Notating Vectors This is how you notate a vector… This is how Text books usually write vector names in bold. This is how you notate a vector… You would write the vector name with an arrow on top. This is how you draw a vector…

Vector Angle Ranges Quadrant II Quadrant I x Quadrant III Quadrant IV y Quadrant II 90˚< θ < 180˚ Quadrant I 0˚< θ < 90˚ θ θ x θ θ Quadrant III 180˚< θ < 270˚ Quadrant IV 270˚< θ < 360˚

Direction of Vectors x θ θ What angle range would this vector have? What would be the exact angle and how would you determine it? Between 180˚ and 270˚ θ x θ Between -270˚ and -180˚

Magnitude of Vectors The best way to determine the magnitude of a vector is to measure its length. The length of the vector is proportional to the magnitude (or size) of the quantity it represents.

Sample Problem

Equal Vectors

Inverse Vectors

Right Triangle Trigonometry

Hypotenuse2 = Opposite side2 + Adjacent side2 Pythagorean Theorem Hypotenuse2 = Opposite side2 + Adjacent side2

Basic Trigonometric Functions

Trigonometric Inverse Functions

Trigonometry Refresher: x q To find the resultant, To find the angle, q

Sample Problem Tree tan 50˚ = width/100 m width = (100 m) tan 50˚ 119 m 155 m width = 119 m R2 = (119 m)2 + (100 m)2 50˚ 100 m R = 155 m

Sample Problem You are standing at the very top of a tower and notice that in order to see a manhole cover on the ground 50.0 meters from the base of the tower, you must look down at an angle 75.0˚ below the horizontal. If you are 1.80 m tall, how high is the tower? tan 75.0˚= height(eye) / 50.0 m 75˚ height(eye) = (50.0 m) tan 75.0˚ height(eye) = 187 m height(building) = 187 m – 1.80 m 75˚ height(building) = 185 m 50 m

END