6 knotts at 15° East of North 5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North 23 cm3

Scalars and Vectors Next, we are going to study motion. Motion of objects can be described by words. Even a person without a background in physics has a collection of words which can be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a sufficient vocabulary for describing the motion of objects. In physics, we use these words and many more. We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration. As we will soon see, these words are associated with mathematical quantities which have strict definitions. The mathematical quantities which are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions

Scalars and Vectors Vectors Scalars Vector = size AND direction Ex: displacement, velocity, acceleration Cannot use normal arithmetic. Ex: 3mi + 2mi = 1mi 3mi + 2mi = 5 mi 3mi + 2mi = 3.6mi Scalar = magnitude or quantity (size) Ex: mass, energy, money, distance Normal Number Can add, subtract, multiply, etc normally. Ex: 3mi + 2mi = 5mi! Scalar is the magnitude or size of something Scalars can be added just like normal numbers – they are normal numbers!

Notation of Vectors (symbol) Angle of vector from positive x-axis Name of vector - Vectors are written with an arrow over the top, or in bold text in your book Magnitude of Vector

45° 2.3

Adding Vectors Graphically Remember: Head to tail Use the white board to show some more examples of adding vectors. Have the students practice a few graphical adding of vectors on their own (make worksheet). Start with vectors going in the same direction, then vectors going in opposite directions, then vectors going at angles to each other. Focus on head to tail method each time.

Vector Components (first, a triangle review)

If C is a vector, then A and B are the vertical and horizontal components Notice how vector C is the resultant vector of vector A and B added together. On the board do a few practice problems finding the components of vectors when given the length of the vector and the angle. Also do a few problems in reverse finding the length and angle of the vector if you know the components. However, we are going to use different notations for B and A…..

However, we are going to use different names for A and B θ Notice how vector C is the resultant vector of vector A and B added together. On the board do a few practice problems finding the components of vectors when given the length of the vector and the angle. Also do a few problems in reverse finding the length and angle of the vector if you know the components. What are the equations for Cx and Cy? 10

θ Practice on board with finding vector components, and finding vectors from components.

Vector Addition Resultant vector Not the sum of the magnitudes Vectors add head-to-tail x-components add to give x-component of resultant y-components add to give y-component of resultant

Adding Vectors by Components

Adding Vectors by Components Transform vectors so they are head-to-tail.

Adding Vectors by Components Bx By A B Ay Ax Draw components of each vector...

Adding Vectors by Components Ay Ax Bx Add components as collinear vectors!

Adding Vectors by Components Ay Ry Ax Bx Rx Draw resultants in each direction...

Adding Vectors by Components Ry q Rx Combine components of answer using the head to tail method...

Adding Vectors by Components Use the Pythagorean Theorem and Right Triangle Trig to solve for R and q…

Challenge: The Strongman...

Adding Vectors…A strategy - Draw the vectors Solve for the components of the vectors Add the x components together Add the y components together NEVER ADD AN X COMPONENT TO A Y COMPONENT! Redraw your new vector Solve for the magnitude of the resultant vector (using Pythagorean Theorem) Solve for the angle of the resultant vector (using tan)

Some Examples Using the Strategy A hunter walks west 2.5km and then walks south 1.8km. Find the hunter’s resultant displacement (distance and direction). A man lost ina maze makes three consecutive dispacements so that at the end of the walk he is right back where he started. The first displacement is 8.00m westward, and the second is 13.0m northward. Find the magnitude and direction of the third displacement. A rock is thrown with a velocity of 23.5m/s at an angle of 22.5 degrees to the horizontal. Find the horizontal and the vertical velocity components. A boat is rowed east across a river with a constant speed of 5.0m/s. If the current is 1.5m/s to the south, what direction must the boat row to get straight across? What is the speed that it makes good?