CONCEPTUAL

1. ___ _ is an example of a scalar quantity

a) velocity

b) force

c) volume

d) acceleration

2. ___ is an example of a vector quantity

a) mass

b) force

c) volume

d) density

3. A scalar quantity:

a) always has mass

b) is a quantity that is completely specified by its magnitude

c) shows direction

d) does not have units

4. A vector quantity

a) can be a dimensionless quantity

b) specifies only magnitude

c) specifies only direction

d) specifies both a magnitude and a direction

5. A boy pushes against the wall with 50 pounds of force. The wall does not move. The aresultant force is:

a) -50 pounds

b) 100 pounds

c) 0 pounds

d) -75 pounds

6. A man walks 3 miles north then turns right and walks 4 miles east. The resultant displacement is:

a) 1 mile SW

b) 7 miles NE

c) 5 miles NE

d) 5 miles E

7. A plane flying 500 MI/hr due north has a tail wind of 45 MI/hr the resultant velocity is:

a) 545 miles/hour due south.

b) 455 miles/hour north.

c) 545 miles/hr due north.

d) 455 MI/hr due south

8. The difference between speed and velocity is:

a) speed has no units

b) speed shows only magnitude, while velocity represents both magnitude (strength) and direction

c) they use different units to represent their magnitude

d) velocity has a higher magnitude

9. The resultant magnitude of two vectors

a) Is always positive

b) Can never be zero

c) Can never be negative

d) Is usually zero

10. Which of the following is not true.

a) velocity can be negative

b) velocity is a vector

b) speed is a scalar

d) speed can be negative

TRUE OR FALSE

1. A vector is a large quantity and a scalar is a small quantity.2. A scalar quantity has a magnitude and a vector quantity does not.3. A vector quantity is described with a direction and a scalar is not.4. Scalar quantities are path dependent quantities and vector quantities are not.5. A scalar quantity depends only upon the initial and final values of the quantity; this is not

the case for vector quantities.6. The quantity 20 m/s, north is a speed and as such is a scalar quantity.7. The quantity 9.8 m/s/s is an acceleration value and as such is a vector quantity.8. Distance is a vector quantity and displacement is a scalar quantity. 9. A person makes a round-trip journey, finishing where she started. The displacement for

the trip is 0 and the distance is some nonzero value. 10. A person starts at position A and finishes at position B. The distance for the trip is the

length of the segment measured from A to B. 11. If a person walks in a straight line and never changes direction, then the distance and the

displacement will have exactly the same magnitude. 12. The phrase "20 mi, northwest" likely describes the distance for a motion. 13. The phrase "20 m, west" likely describes the displacement for a motion. 14. Velocity is a vector quantity and speed is a scalar quantity.15. Acceleration is a vector quantity.16. The direction of the acceleration vector is dependent upon two factors: the direction the

object is moving and whether the object is speeding up or slowing down.17. Length, area and volume are scalar quantities.18. Pressure, temperature and entropy are vector quantities.19. Displacement is a vector quantity.20. Momentum and velocity are vector quantities.

CONCEPTUAL1. The magnitude of an object's average velocity can ONLY equal the magnitude of its

average speed when the object is __________.2. A scalar is a quantity that can be completely described by stating its

a. SIZEb. DIRECTIONc. SIZE AND DIRECTION

3. Which quantity is NOT a scalar?a. Timeb. Accelerationc. Massd. Distance

4. During a 30 minute period of time, one car moves at a constant velocity of 45 mph, N, while a second car moves at a constant velocity of 45 mph, W. During this time interval, the cars would have the same __________.a. Instantaneous speed b. Instantaneous Velocity c. Displacement d. acceleration

5. Used to describe one dimensional quantities.6. Location in place and space, velocity, acceleration are _______ quantities.7. Used to describe multi-dimensional quantities.8. Vectors are described by ________ and 9. ________.10.Both scalar and vector have _______.

SCALAR OR VECTOR1. 256 bytes2. 1500 calories3. 25 m/sec, east4. 4 mi., north5. 3o C6. 78o F7. 21 km8. 55 kph, east9. 1 terabyte10. 700 mb

PROBLEMS

1. Find the polar coordinates r and θ of a point P having Cartesian coordinates x = 3 and y = 6.

2. What is the distance between point P having Cartesian coordinates (2,5) and point Q having coordinates (5,9)?

3. What are the polar coordinates of point Q in the previous question?4. What angle does the segment PQ make with the axis Ox in the previous question?5. What is the distance from the origin to point Q in practice problem 2?6. A point P has the following coordinates in a cylindrical system: (3,30°,5). Find the

coordinates in a Cartesian 3-D system.7. What is the distance from point P to the origin in practice problem 6?8. A point P in a horizontal plane has coordinates (–3.50,6.20) meters. Find the polar

coordinates of this point.9. Find the magnitude of the following vectors: (3.0,–5.0,6.0) meters and (20,45,–30) N.10. Is it possible for a vector to have zero magnitude but nonzero components? Explain11. In Figure 2.12, which vectors are equal? Explain.12. Let A = 2.0 i + 3.0 j and B = 3.0 i –2.0 j. Using the properties of unit vectors i, j, and k,

find the components of the vector C = A × B.13. Calculate A · B for the vectors in problem 12. What can you say about the directions of A

and B?14. Calculate A · C and B · C for the vectors in problem 12. What can you say about their

directions?15. For the vectors in problem 12, calculate A + B and B – A. What are the magnitudes of

these two new vectors?16. What can you say about the directions of the vectors calculated in problem 15?17. Calculate the magnitude of vector C in problem 12.18. A hiker walks 53.1 degrees north of east for 2.5km then due east for 2.0km. What is her

total displacement from her starting point if you measure the distance along a straight line?

19. A telephone pole support cable is in the way of some construction workers. In order for the work to proceed, the cable must be moved 2 meters closer to the pole. If the pole is 10 meters tall and the cable is currently fastened to the ground 8 meters from the pole, how much will the workers need to cut off from the cable when they move it?

20. A bike messenger traveled 3 blocks North, 6 blocks East, 6 blocks South, and finally 9 blocks West in order to deliver a package in the traffic, congested city. If his trip took 39 minutes, what was the magnitude of his average velocity in blocks/minute?

21. If the messenger in Question #20 could have traveled directly to his destination, what would have been the direction of his net displacement?

22. A family taking a vacation traveled 6 hours at 65 mph and then 3 hours at only 49 mph. What was their average speed during this trip?

23. A student warming up for practice travels one full circuit, 400 meters, around the track. Initially he jogs 78 meters at 1.5 m/sec, then runs 234 meters at 2.2 m/sec, and finally cools down by finishing the final 88 meters at 1.0 m/sec. What was his average speed?

24. What was the student's average velocity in Question #23?

25. – 26. Coach Sweeney walks 26 yards to the north along the sideline, pauses, and walks 12 yards back to the south.

a. Determine the distance which Coach moved.b. Determine Coach's resultant displacement.

27. Rosa Boat is paddling upstream at 1.25 m/s relative to the water in a river which is flowing at 0.50 m/s relative to the banks of the river. What is the resultant velocity of Rosa's boat (relative to the banks)?

28. Rosa Boat is paddling downstream at 1.25 m/s relative to the water in a river which is flowing at 0.50 m/s relative to the banks of the river. What is the resultant velocity of Rosa's boat (relative to the banks)?

29. The takeoff speed of a military aircraft from an aircraft carrier is approximately 170 mi/hr relative to the air. They acquire this speed through a combination of a catapult system present on the aircraft carrier and the aircraft's jet propulsion system. A common strategy is to head the carrier and the plane into the wind. If a plane is taking off from an aircraft carrier which is moving at 40 mi/hr into a 20 mi/hr headwind, then what speed relative to the deck of the aircraft carrier must it obtain to takeoff?

30. Claire de Iles is shopping. She walks 16 m to the end of an aisle. She then makes a right hand turn and walks 21 m down the end aisle. Determine the magnitude of Claire's resultant displacement.

31. Jim Nazium is walking from lunch to his PE class. He exits the lunchroom and walks 43 m west. He then turns and walks 72 m north down the hallway leading to the locker room. Determine the magnitude and direction of Jim's resultant displacement.

32. On her trip from home to school, Karla drives along three streets after exiting the driveway. She drives 1.85 miles south, 2.43 miles east and 0.35 miles north. Determine the magnitude of Karla's resultant displacement

33. Sheila is captain of the Varsity cross country team. During the after-school practice on Tuesday, she led the team on the following run from school to a nearby park where they met the coach for a meeting: 0.68 miles, north; 1.09 miles east; 1.56 miles north; 0.32 miles, west. Determine the magnitude and direction of the team's resultant displacement.

34. During the Vector Addition lab, Mac and Tosh start at the classroom door and walk 40.0 m, north, 32.5 m east, 15.5 m south, 68.5 m west, and 2.5 m, north. Determine the magnitude and direction of the resultant displacement of Mac and Tosh.

35. Avery, the quarterback of South's Varsity football team, made the most amazing pass in the Homecoming game against cross town rival North. He threw the pass from the exact center of the field to the corner of the end zone, where Jamaal caught it for the game winning score. If the

football field is 160 feet wide (sideline to sideline) and it is 60 yards from midfield to the back of the end zone, then how far did the ball travel from Avery's hands to Jamaal's hands.

36. A spelunker (person who explores caves) determines that the cave entrance is located 349 m, 253° from her current position. How far south and how far west from her current position is the cave entrance?

37. Avery, South's quarterback, throws a pass 36.5 yards at 21° W of S before it is caught by Mitchell with a diving catch. Assuming that the field runs north and south, and that Avery threw the pass from 7.2 yards behind the line of scrimmage, how many yards were gained on the play?

38. An airplane begins its journey into Canada from a destination located 285 mi south of the border. The plane flies along a straight-line path at 189 mi/h in a direction of 20.5 degrees west of north. Determine the number of minutes before the plane crosses the border. Assume that the border is aligned directly east and west in the region where the flight takes place.

39. Ima Peode wishes to throw a 2.8-kg pumpkin horizontally off the top of the school roof in order to hit Mr. H's car. The car is parked a distance of 13.4 m away from the base of the building below the point where Ima is standing. The building's roof is 10.4 m high. Assuming no air resistance, with what horizontal speed must Ima toss the pumpkin in order to hit Mr. H's car

40. – 41. Albert is South’s star punter for the varsity football team. His best hang time this past season was for a punt which he kicked at 74° above the horizontal. The punt had a 6.2 second hang time.

a. Determine the speed at which the ball was punted.b. Determine the horizontal distance which the ball traveled.

42. In an apparent effort to earn an appearance on the Destroyed in Seconds show, Caleb attempts a bicycle maneuver in which he jumps between two ramps whose elevated edges are located a distance of 1.8 meters apart. The ramps are angled at 35° and located at the same height. Determine the speed (in m/s and mi/hr) that Caleb must acquire to accomplish this stunt. (Given: 1.00 m/s = 2.24 mi/hr)

43. On New Year’s eve of 2007, Robbie Maddison set the world record for the longest motorcycle jump, traveling 98.3 m through the air from ramp to ramp. (The record has since been broken several times by Maddision himself.) Assuming a launch angle of 45°, insignificant air resistance and a landing location at the same height as the launch height, determine the speed with which Maddison left the ramp

44. The La Quebrada Cliff Divers provide daily entertainment for the crowds at Acapulco, Mexico. As a group of professional high divers, they dive off the cliff of La Quebrada and fall 45.1 m (148 feet) to the water below. More than an act of bravery, the cliff divers must time their dive so that they hit the water when the crest of an incoming wave has arrived. Determine the speed with which Pedro must run off the cliff in order to land in the water a horizontal distance of 17.8 m from the edge of the cliff.

45. An emergency relief plane is dropping a care package from a plane to a group of medical personnel working for a relief agency in an African village. The package is designed to land in a small lake, inflate an attached raft upon impact, and finally resurface with the raft side down. The plane will be moving horizontally with a ground speed of 59.1 m/s. The package will be dropped a horizontal distance of 521 m from the intended target location. At what altitude above the pond must the plane be flying in order to successfully accomplish this feat?

46. Taylor and Drew finish their last class on the day before Spring break and decide to take a spontaneous road trip. Their trip involves the following movements:

42 miles, 67° north of west (113° CCW)61 miles, west23 miles, 17° west of south (253° CCW)

Taylor's car breaks down after the last leg of the trip. How far and in what direction are Taylor and Drew from campus?

47. Dora is exploring a cave. She starts at the entrance and makes the following straight line movements:

68 m, south112 m, 25° north of west (155° CCW)34 m, south182 m, 17° south of east (343° CCW)

Determine Dora's position relative to the entrance of the cave. That is, how far and in what direction is Dora from the cave entrance?

48. – 49. A weather report shows that a tornado was sighted 12 km south and 23 km west of your town. The storm is reported to be moving directly towards your town at a speed of 82 km/hr.

a. What distance from your town was the tornado sighted?b. Approximately how much time (in minutes and hours) will elapse before the violent storm arrives at your town?

50. Mia Ander exits the front door of her home and walks along the path shown in the diagram at the right (not to scale). The walk consists of four legs with the following magnitudes:

A = 88 mB = 272 mC = 136 mD = 183 m

Determine the magnitude and direction of Mia's resultant displacement.