You Know? Do You Know? Do You Know?

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1 Phyz Questions and Problem Set VECTORS AND MATH. Name: You Know? Do You Know? Do You Know? B A S I C C O N C E P T Q U E S T I O N S INSTRUCTIONS: The following questions require written responses. Answers may include diagrams and/or references to equations. Respond in complete sentences and include a statement of the question in your response. Leave at least one blank line between your answers. Vectors and Scalars (a first look) / Scalar Multiplication of Vectors 1. What is a vector? How does a vector differ from a scalar? 2. Do the terms vector and scalar refer to a type of physical quantity or a type of unit of measure? 3. A physical quantity called impulse is defined as the change in momentum. Is impulse a vector or a scalar? Explain your reasoning. Polar Coordinates / Rectangular Coordinates 4. How do polar and rectangular representations of vectors differ? 5. Could a single vector be described both in polar and rectangular components? Why or why not? 6. Into which quadrant I, II, III, or IV is each vector directed? a. a = (2m, 5m) b. b = (4N, -7N) c. c = (-12m/s, 9m/s) d. d = (-90N, -20N) 7. Into which quadrant I, II, III, or IV is each vector directed? a. a = (2m; 345 ) b. b = (4N; 234 ) c. c = (12m/s; 52 ) d. d = (90N; 148 ) Vector Addition 8. Consider the following vectors: a = (10m, 20m), b = (15m, 25m). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain. 9. Consider the following vectors: a = (10m, 20m), b = (15ft, 25ft). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain. 10. Consider the following vectors: a = (10m, 20m), b = (15m/s, 25m/s). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain. 11. Consider the following vectors: a = (10m, 20m), b = (15m; 25 ). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain. 12. Consider the following vectors: a = (10m; 20 ), b = (15m; 25 ). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain.

2 13. Consider the following vectors: a = (10m; 20 ), b = (15N; 25 ). Can these vectors be added as they are right now? Can they be added after a conversion of some sort? If so, describe the required conversion. If not, is it impossible to add these two vectors? Explain. 14. Consider two vectors, one with a magnitude of 9m and the other with a magnitude of 4m. The direction of each vector can be adjusted to fit the conditions specified below. a. What is the magnitude of the greatest vector that could result from combining these vectors? b. What is the magnitude of the smallest vector that could result from combining these vectors? 15. Consider two vectors: one has a magnitude of 3m and the other has a magnitude of 4m. On your paper, show how the two vectors could be combined to give: Speed a. a resultant with a magnitude of 7m. b. a resultant with a magnitude of 1m. c. a resultant with a magnitude of 5m. (Yes, it can be done!) 16. What is meant by saying motion is relative? For everyday motion, what is motion relative to? 17. Speed is the rate at which what happens? 18. What is the difference between instantaneous speed and average speed? 19. Does the speedometer of a car read instantaneous speed or average speed? Velocity 20. What is the difference between speed and velocity? 21. What is the difference between instantaneous velocity and average velocity? 22. If the speedometer in a car reads a constant speed of 50mph, you can say that the car has a constant speed but you can't say that it has a constant velocity. Why is this? 23. Which two controls on a car enable a change in speed! Name another control that enables a change in velocity (without a change in speed.

3 Smooth Operations E Q U A T I O N M A N I P U L A T I O N E X E R C I S E S Speed INSTRUCTIONS: Solve the following exercises by writing out the appropriate equation, rearranging it and/or substituting given values into it as indicated. Diagrams may be helpful but are not required unless otherwise specified. Draw a box around your final answer. You may write solutions "two-across" on your paper (but no more than two across). 24. Rewrite the equation for uniform motion (v = x/t) a. solving for x b. solving for t 25. a. If x = 100m and t = 20s, determine v. b. If v = 9m/s and t = 20s, determine x. c. If x = 40m and v = 8m/s, determine t. Vector Addition Consider the vectors given below. a = (2m, -7m) b = (-5m, 3m) c = (9m, 4m) d = (-1m, -6m) e = (12N, 8N) 26. Complete the following vector addition problems. Use vectors listed above. a. z = a + b b. x = 4b + 3c c. w = 5c + 2e 27. Complete the following vector subtraction problems. Use vectors listed above. a. z = a - b b. x = 4b - 3c c. w = 5c - 2e 28. Resolve each polar vector into rectangular components. a. (7m; 70 ) b. (12N; 144 ) c. (200kg-m/s; 200 ) d. (81m/s; 327 ) Composing Vectors (converting from rectangular to polar form) 29. Compose the following vectors from rectangular to polar form. a. (12m, 5m) b. (-16N, 12N) c. (-12m, -5m) d. (16N, -12N) 30. Add the following vectors, show answers in polar form. a. (10m; 50 ) + (10m; 50 ) b. (6N; 130 ) + (12N; 250 ) c. (16m; 315 ) + (12m; 135 ) d. (30N; 222 ) + (20N; 333 ) 31. Consider the vectors shown in the diagram to the right. Each is 8.0m long. What is their sum? (Be Careful!) 105 o 30 o

4 Mysteries of the Universe GEDANKEN QUESTIONS / UNDERSTANDING THE WORLD AROUND YOU INSTRUCTIONS: The following questions require written responses. Answers may include diagrams and/or references to equations. Respond in complete sentences and include a statement of the question in your response. Leave at least two blank lines between your answers. 32. Moonshot. In 1969, three Apollo astronauts left Cape Canaveral, went to the moon and back, and splashed down in the Pacific Ocean. An admiral bid them good-bye at the Cape and then sailed to the Pacific Ocean in an aircraft carrier where he picked them up. Compare the displacements of the astronauts and the admiral. 33. Walkin the dog. You have an annoying dog that likes to chase sticks. In order to keep it preoccupied for the longest time between throws, should you throw the stick in front of you, behind you, to the side of you, or doesn't the direction make any difference? Explain your answer. Assume you continue walking. 34. Goin home. Where would Nanook have to live in order to walk 1 mi South, then 1 mi East, then 1 mi North to return home? Why? 35. Nowhere fast. Kari runs 8 m/s yet after 10 s, she hasn t gone anywhere. How is this possible? 36. Average Speed. If you get caught in a traffic jam and don t move, then you drive 15 miles in the next 15 minutes (averaging 60 mph), can you say that you averaged 30 mph for the whole trip? Why or why not?

5 Welcome to the Real APPLICATION PROBLEMS INSTRUCTIONS: Solve the following problems in accordance with the Official Problem Solving Guidelines: 1. Draw a diagram, 2. List quantities, 3. Write base equation(s). 4. Rearrange equation(s), 5. Substitute quantities, 6. Write out (and box) final answer. No more than two problems may be solved on a single side of paper. Average Speed 37. If you were to walk with a speed of 3.0 m/s for 2.0 hours, you would be very tired. How far would you have walked? 38. a. If it took 100 minutes for Mr. Sullivan to drive from Lake Arrowhead to his hair stylist in Simi Valley (a distance of 90 miles), what was his average velocity during the trip? b. Mr. Loewen averaged 75mi/hr for the same trip. How long was Loewen on the road (in minutes)? 39. The speed of light is 3.0xl0 8 m/s. How long does it take light from the sun to reach the earth (the distance between the earth and the sun is 1.47x10 11 m). 40. a. How far is a light-year (the distance light travels in a year)? b. How far is a light-nanosecond? 41. An arrow is shot at Mr. Vaughan 50.0m away. You hear Mr. Vaughan scream in pain 0.500s after releasing the arrow. What was the speed of the arrow as it traveled to the target? (The speed of sound is 343m/s you will need to use that information.) 42. A car travels at 30m/s for 100s, at 20m/s for the next 100s, and finally at 25m/s for 50s. Find its average speed for the entire trip. What s The Vector Victor? 43. What is the displacement vector of a knight in chess if the knight moves two squares to the right and one square up and the chess board has 2.5cm x 2.5cm squares. a) in rectangular components (x- and y-displacements)? b) in polar components (distance and angular direction)? 44. The steps on the bleachers are 15 cm high by 40 cm deep. If you could walk up 20 steps find the total displacement... a) in rectangular components b) in polar components 45. A person walks 70m to an elevator and then ascends 40m. Find the magnitude and direction of the person's displacement from the starting place. 40 cm 15 cm 46. Coach Craft becomes lost and drives 12km west, 5km south, and then 8km east. Find the magnitude and direction of the car's displacement from the starting place.

Bonus Problems: Speed 47. Kym jogs halfway to her destination at 6m/s and walks the rest of the way at 4m/s. What is her average speed for the entire trip? (Hint: It's not 5m/s.) 48.

6 Bonus Problems: Speed 47. Kym jogs halfway to her destination at 6m/s and walks the rest of the way at 4m/s. What is her average speed for the entire trip? (Hint: It's not 5m/s.) 48. A car covers one quarter of distance to the next town at 10m/s, another quarter at 15m/s, and the rest at 30m/s. Find the car's average speed for the entire trip. 49. A man drives one third the distance home at 7m/s. How fast must he drive the rest of the way so that his average speed is 10m/s? Vectors 50. Two cars leave an intersection at the same time, one headed north at 14m/s and the other headed east at 19m/s. How far apart are they after half an hour? 51. The resultant of two perpendicular forces has a magnitude of 40N. If the magnitude of one of the forces is 25N, what is the magnitude of the other? 52. The yacht Irish Coffee is heading north at l0m/s in a tidal stream that is flowing 5m/s to the east. What is the magnitude and direction of the boat's velocity with respect to the earth's surface? 53. The ketch Minots Light is heading northwest at 7m/s in a tidal stream that is flowing 3m/s to the southwest. What is the magnitude and direction of the boat's velocity with respect to the earth's surface? 54. Mr Ochs rows a boat heading straight across the Mississippi River at a point where it is 800m across. Due to the river current, he ends up 600m downstream, a. How far is his landing point (2) from his starting point (1)? b. On his next trip, he wishes to land directly opposite from his current position. In what direction should he head to get from point 2 to point 3? 55. The shadow of an airplane taking off moves along the runway at 47m/s. If the sun is directly overhead and the airplane's speed is 60m/s, what is the angle of ascent? 56. The following forces act on an object resting on a level, frictionless surface: 10N to the south, 20N to the east, 10N at an angle 40 south of east, and 20N at an angle 50 west of south. Find the magnitude and direction of the net (resultant) force acting on the object. Sources The Book of Phyz by Dean Baird, Dean Baird Physics by Arthur Beiser, Addison-Wesley Conceptual Physics: A High School Program by Paul Hewitt, Addison-Wesley Physics by Douglas Giancoli, Douglas Giancoli, Prentice-Hall Fundamentals of Physics by Halliday and Resnick, John Wiley & Sons College Physics by Serway and Faughn, Saunders College Publishing Physics by Jerry Wilson, D.C. Heath t Thinking Physics by Lewis Epstein, Insight Press ft The Flying Circus of Physics by Jearl Walker, John Wiley & Sons t Physics in the Real World by Keith Lockett, Cambridge University Press

Chapter 2 Describing Motion

Chapter 2 Describing Motion Chapter 2 Overview In chapter 2, we will try to accomplish two primary goals. 1. Understand and describe the motion of objects. Define concepts like speed, velocity, acceleration,