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##### Unit 3: Motion

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**Unit 3: Motion**Introduction to Vectors**B. Vectors**• Scalar units of measurement that involve no direction (mass, volume, time). • Vector a physical quantity having both magnitude and direction (displacement, velocity, acceleration).**Distance vs Displacement**• distance-- a scalar quantitythat refers to how far an object has moved during its motion. • displacement is a vector quantitythat refers to how far out of place an object is; it is the object's change in position.**To test your understanding of this distinction, consider the**motion depicted in the diagram below. A science teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.**Assignment**• Distance vs Displacement (9-14)**Determining Angles**• Before we move on to learn these methods we should learn about angles and direction**Angles**• There are two ways to show direction • Compass direction • RCS system**Assignment**• Finding Directions**Sample Problem A A helicopter takes off from a point A**and flies due east 30km and then lands. If the helicopter takes off again and flies 40km in a straight line, how far is it from its original position? We don’t have enough information, so let’s consider the possibilities.**1) If both displacements are in the same direction, the**displacement would be: 30km 40km 30km + 40km = 70km east**2) If displacements are in opposite directions, the**helicopter would be 10km west of it’s start 30 km 40 km 30km east + 40km west = 10km west**3) If the helicopter went due north after landing, the**problem gets tougher. R 40 km 30 km • R represents the resultant vector. (the displacement of the helicopter) • There are 2 ways to solve this- TIP TO TAIL METHOD or VECTION ADDITION METHOD**1.Vector Addition - Tail to Tip Method:**• 1.) Start by placing any vector with its tail at the origin • 2.) Place the tail of another vector to the tip of the previous vector • 3.) After placing all the vectors in this fashion, the resultant vector is found by drawing a straight line from the tail of the first vector to the tip of the last vector.**Ex.**• Given the following vectors, find the resultant vector. • ** NOTE: Order of placement (addition) does NOT matter!**Animation to show vector placement**• http://www.physicsclassroom.com/mmedia/vectors/ao.cfm**Sample Problem B **A man walks 6 blocks east and then 8 blocks south. What is the resultant displacement? (Solve using the vector addition method) Step 1 choose a suitable scale. 1cm = 1 block Step 2 draw your diagram, make sure that it is accurate**6 Blocks [E]**8 blocks [S] R Step 3 measure the resultant vector. In this example, R is 10cm long, therefore the displacement is 10 blocks. To find the direction, use your protractor. You should find that the displacement is 217o**Assignment**• Tip to Tail (graphical) Vector addition**2. Mathematical Vector Addition**• This method will give much more accurate results • If two vectors are at right angles to each other, R can be calculated using the Pythagorean Theorem • a2 + b2 = c2**Sample Problem 1 A pilot is flying north at a speed of**80km/h however the wind is blowing at 40km/h from west to east. Determine the velocity of the plane mathematically. To find magnitude, we use: a2 + b2 = c2 402 + 802 = c2 1600 + 6400 = c2 8000 = c2 √8000 = √c2 c = 89.4km/h 40 km/h [E] 80 km/h [N] R θ**Sample Problem 2 A boat crosses a river at a velocity of**26.3 km/h [S]. If the river is flowing a velocity of 5.6 km/h [W], what is the resultant velocity of the boat? If the boat travels at this velocity for 15 minutes, what is the displacement of the boat?**θ**a2 + b2 = c2 5.62 + 26.32 = c2 31.36 + 691.69 = c2 723.05 = c2 √723.05 = √c2 c = 26.9km/h R 26.3 km/h [S] 5.6 km/h [W]**Assignment**• Mathematical addition of vectors