7.5 Vectors and Applications Day 1 Thurs March 12 Do Now Find the absolute value of the complex number

Quiz Review Retakes by next Wed

Magnitude and Displacement Some quantities are measured only by their magnitude – Time, length, mass, etc Other quantities are measured by a magnitude and a direction – Displacement, velocity, force

Vectors When both magnitude and direction are measured, together they describe a vector A vector in the plane is a directed line segment. Two vectors are equivalent if they have the same magnitude and direction

Properties of Vectors Each vector has an initial point and a terminal point – The direction of the vector goes towards the terminal point – We can compare slopes of vectors to determine if the direction is the same The length, or magnitude, of a vector is expressed with absolute value lines – Use the distance formula to find the magnitude

Ex Ex1 on p.647 of book

You try Given the points D(-1,-1) J(3,1) O(0,0) F(2,1) sketch each vector and determine if they are equivalent

Vector Addition The sum of two vectors is the vector needed to travel both vectors in order The sum is also called the resultant of the vectors

Ex Forces of 15 newtons and 25 Newtons act on an object at right angles to each other. Find their sum, giving the magnitude of the resultant and the angle that it makes with the larger force

Closure Given the points C(-2,5) G(-4,4) O(0,0) F(2,1) Sketch the pair of vectors and determine whether they are equivalent HW: p.652 #1-15 odds

7.5 Vector Addition Day 2 Fri March 13 Do Now Solve the triangle ABC given A = 90 deg, b = 25, c = 15

HW Review: p.652 #1-11

Ex An airplane travels on a bearing of 100 deg at an airspeed of 190 km/h while a wind is blowing 48km/h from 220 deg. Find the ground speed of the airplane and the direction of its track

Components Given a vector W, the vectors U and V are called components of W if U + V = W Finding the components is called resolving, or representing a vector To find components, we usually want to look for perpendicular components, then use trig equations to find the vectors

Ex A vector W has a magnitude of 130 and is inclined 40 degrees with the horizontal. Resolve the vector into horizontal and vertical components

Ex A wooden shipping crate that weights 816lb is placed on a loading ramp that makes an angle of 25 deg with the horizontal. To keep the crate from sliding, a chain is hooked to the crate and to a pole at the top of the ramp. Find the magnitude of the components of the crate’s weight (disregarding friction) perpendicular and parallel to the incline

Closure Two forces of 50N and 60N act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force HW: p.652 #17-37 odds

7.5 Vectors and Applications Day 3 Mon March 16 Do Now Two forces of 255N and 325N act on an object. The angle between the forces is 64 deg. Find the magnitude of the resultant and the angle that it makes with the smaller force

HW Review: p.652 #13-37 odds

Closure What is a vector? What do they measure? HW: none