COLLEGE PREP PHYSICS

QOTD You and your classmates are all given a treasure map. You REALLY want that treasure! You are given a series of steps to follow including the number of meters to travel before each turn. What can you do to get there first?

TSWBAT distinguish between a scalar and a vector. Scalar- a physical quantity that has magnitude. Ex: Vector- a physical quantity that has both magnitude and direction. Ex: Represented by arrows –> length=magnitude direction=direction Printed in boldface or drawn with arrows above the numbers

TSWBAT add and subtract vectors by using the graphical method. Vectors in 1-D: > > = > 5m/s E + 5m/s E = 10 m/s E *plane’s velocity + tailwind = resultant velocity > + 5m/s E + 3m/s W = 2m/s E *plane’s velocity + headwind = resultant velocity

Graphical Method Vectors in 2-D: When utilizing the graphical method, follow these steps: 1. Define your scale 2. Draw your vectors using the tip-to-tail method. 3. Draw the resultant vector. 4. Measure the vector and the angle. 5. Describe the direction in terms of degrees and direction (N, N of E, W, W of S, etc)

Graphical Method

Vector Activity Use a ruler and a protractor to calculate the resultant vector in each of the following problems: 1. A person walks 5.0 meters east and 12.0 meters at 60 degrees north of east. Find the magnitude and direction of the resultant displacement. deg.) 2. A boat moves with a velocity of 2m/s North when it encounters a gust of wind with a velocity of 2 m/s west. What is the resultant velocity of the boat? (Include the angle)

Sample Problem You are running to physics class because you just can’t wait to get there and learn more about vectors! To get to class, you run 2m North, 7m West, and 1m South. 1) What was the total distance you travelled? 2) What was your displacement from start to finish? Include the angle and direction in your answer.

Parallelogram Method When solving for the resultant of two vectors…you can also use the parallelogram method. 1. Draw the vectors starting from the origin. 2. Complete the parallelogram. 3. Draw the vector from the start corner to the end corner.

Sample Problem A boat moves with a velocity of 5m/s east (across a river). The river flows south with a velocity of 2m/s. What is the resultant vector?

Trigonometry is your friend. To calculate the resultant vector of a right triangle… 1. Use the Pythagorean Theorem to find the magnitude of the vector. (vector’s sketched tip to tail) 2. Use a trigonometric function…sine, cosine, tangent…to find the angle. 3. Use N, S, E, W, N of E, etc. to describe the direction of the angle.

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Analytical Method (Trig) A boat travels Eastward at 8m/s across a river that is flowing southward at 7m/s. What is the resultant velocity of the boat?

Finding the resultant for vectors not at 90 degrees… Graphical method can be :0 There is another way for vectors at angles other than 90 degrees! Law of Cosines!! Hooray for Math!!!! Law of Cosines: R 2 = A 2 + B 2 -2ABcosѳ

Now the reverse… Calculating the components of a vector: 1. The resultant is now given. 2. Find the x component of the vector using trig. 3. Find the y component of the vector using trig.

Finding Resultant For multiple vectors… 1. Find the x and y components for each of the vectors. 2. Add all the x components. 3. Add all the y components. 4. Make a right triangle from the sum of x and the sum of y. 5. Find the resultant using trig or graphical. (trig is easier)

Example problem