Grade Level Physics
Unit 2: Vectors
Conceptual Physics Vectors Outline
Texas Physics: Chapter 2 pg 38-40 and Chapter 3 pg 82-94
Fill in the Charts completely
Variables introduced or used in chapter:
Quantity
Symbol
Change
∆
Distance covered
d
Displacement
∆d
Elapsed time
∆t
Change in velocity
Acceleration
acceleration due to gravity
Vector
Units
None
M
None
Formula Chart*
*In Class, we will use x for horizontal motion, and y for vertical motion instead of ‘d’
Pythagorean Theorem
Horizontal Component
Vertical Component
Define the following terms using COMPLETE SENTENCES:
Linear Motion
Nonlinear Motion
Independent variable
Vector Quantity
Scalar Quantity
Components of a Vector
Graphical Addition of Vectors
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Grade Level Physics
Unit 2: Vectors
Resolution
Vector
Horizontal Component
Vertical Component
Answer Questions in Complete Sentences:
1. Name some variables that are considered vectors (may have to look this up)?
2. What is the horizontal component of the vector ?
3. What is the vertical component of the vector?
What if R is a displacement vector – does the process of adding vectors or resolving vectors change if R is a
displacement vector or velocity vector?
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Grade Level Physics
Unit 2: Vectors
Unit 3: Vector Homework Problems
Drawing Vectors – Conceptual
1. Could a vector ever be shorter than one of its components? Could it ever be equal in length to one of its
components? Explain your thinking.
2. Which of the following actions is permissible when you are graphically adding one vector to another:
move the vector, rotate the vector, change the vector’s length?
3. Using a coordinate system (system of degrees) how is the angle or direction of a vector determined with
respect to the axes of the coordinate system?
4. The Pythagorean theorem is written a2 + b2 = c2. If you use this relationship to solve vector problems,
what do a, b, and c represent? Be specific.
5. A vector drawn 15cm long represents a velocity of 30 m/s. How long should you draw a vector to
represent a velocity of 20 m/s?
6. A vector that is 1 cm long represents a displacement of 5 km. How many kilometers are represented by a
3 cm vector drawn to the same scale?
7. What is the largest possible displacement resulting from two displacements with magnitudes 10 m and 25
m? What is the smallest possible resultant? Draw sketches to illustrate your answers.
Drawing Vectors - For each vector, select a scale and draw the vector to that scale. Be sure to label both the
magnitude and the direction of the vector, and the scale for each vector.
8.
9.
10.
11.
12.
15 N at 45º
3 lbs at 150º
10 lbs at 50º
7 m/s at 270º
75 ft/s at 345º
Vector Addition
13. A car is driven 125 km due west, then 65 km due south. What is the magnitude of its displacement? (140
km)
14. A shopper walks from the door of the mall to her car 250 m down a lane of cars, then turns 90º to the
right and walks an additional 60 m. What is the magnitude of the displacement of her car from the mall
door? (300 m)
15. A hiker walks 4.5 km in one direction, then makes a 90º turn to the right and walks another 6.4 km. What
is the magnitude of her displacement? (7.82 km)
16. What is the magnitude of your displacement when you follow directions that tell you to walk 225 m in
one direction, make a 90º turn to the left and walk 350 m, then make a 90º turn to the right and walk 125
m? (494.97 m)
17. A car is driven 125 km due west, then 65 km due south. What is the magnitude of its displacement?
18. A shopper walks from the door of the mall to her car 250 m down a lane of cars, then turns 90º to the
right and walks an additional 60 m. What is the magnitude of the displacement of her car from the mall
door?
19. A car moves 65 km due east, then 45 km due west. What are the magnitude and direction of its
displacement? (20 km East OR 20 km @ 0°)
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Grade Level Physics
Unit 2: Vectors
Relative Velocities
20. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the front of the bus
at 4.0 m/s relative to the bus. What is your speed relative to the street? (6.0 m/s relative to the street)
21. You are riding in a bus moving slowly through heavy traffic at 2.0 m/s. You hurry to the back of the bus
at 4.0 m/s relative to the bus. What is your speed relative to the street? (-2.0 m/s relative to the street)
22. A motorboat heads due east at 11 m/s relative to the water across a river that flows due north at 5.0 m/s.
a. What is the velocity of the motorboat with respect to the shore? (12 m/s)
b. What is the direction of the motorboat with respect to due East? (24º)
23. A plane has a northward bearing (90º) and flying at 250 km/h. It soon encounters another crosswind, this
time blowing with a speed of 60 km/h at 180º with respect to the ground. What is the plane’s new
velocity with respect to the ground? (257.10 km/h, 103.5°)
24. An airplane flies due west at 185 km/h with respect to the air. There is a wind blowing at 85 km/h north.
a. What is the plane’s speed with respect to the ground? (203.6 km/h)
b. What is the plane’s direction with respect to the ground? (155º)
25. An airplane flies at 450 km/h west, and encounters a 90 km/h crosswind from the south. What is the
magnitude of the plane’s velocity resultant? (458.9 km/hr)
26. A motorboat heads due east at 15 m/s relative to the water across a river that flows due east at 25 m/s.
What is the velocity of the motorboat with respect to the shore? (40 m/s, east)
27. A motorboat heads due east at 15 m/s relative to the water across a river that flows due west at 25 m/s.
What is the velocity of the motorboat with respect to the shore? (10 m/s, east)
28. An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h to the
west relative to the ground. What is the plane’s velocity with respect to the ground? (167.7 km/hr, 116.6°
)
29. You are in a canoe paddling directly upriver (north) at a speed of 6.5 m/s relative to the water. Viewers
on the shore find that it is moving at only 0.5 m/s, north relative to the shore. What is the speed of the
river? (6.0 m/s, south)
30. You are in a canoe paddling directly upriver (north) at a speed of 12.6 m/s relative to the water. Viewers
on the shore find that it is moving at 20 m/s relative to the shore. What is the speed of the river? (7.4 m/s,
north – with the boat)
31. After being blown off course, an airplane regains its northward bearing (90º) and resumes flying at 235
km/h. It soon encounters an easterly crosswind, this time blowing with a speed of 80 km/h. What is the
plane’s new velocity with respect to the ground?(248.2 km/hr, 71.2 °)
Vector Resolution
32. A bus travels 23.0 km on a straight road that is 30º north of east. What are the east and north components
of its displacement? (east = 1.19 km, north = 11.5 km)
33. What are the components of a vector of magnitude 1.5 m at an angle of 35º? (1.2 m, 0.86 m)
34. A hiker walks 14.7 km at an angle of 325º. Find the east and south components of this walk. (12 m, 8.4
m)
35. An airplane flies at 65 m/s at 149º. What are the west and north components of the plane’s velocity? (56
m/s, 33 m/s)
36. A golf ball, hit from the tee, travels 325 m at a direction of 335°. What are the east and south components
of its displacement? (295 m, 137 m)
37. A car has a velocity of 50 km/h at 60°. Which component of the velocity vector is larger, the x or the y?
38. A bus travels 23.0 km down I-10 at 30° in 2 hours. What are the east and north components of its
displacement? (19.92 km, 11.50 km)
39. What are the components of a vector of magnitude 1.5 m at an angle of 95º? (0.13 m, 1.49 m)
40. A hiker walks 14.7 km at an angle of 325º. Because he isn’t tired enough at the end of his hike, he decides
to calculate the east and south components of his walk. What are they? (12.04 km, 8.43 km)
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Grade Level Physics
Unit 2: Vectors
Unit 3 Vectors Review
Drawing Vectors – Conceptual
1. A vector drawn 15cm long represents a velocity of 30 m/s. How long should you draw a vector to
represent a velocity of 20 m/s?
2. A vector that is 1 cm long represents a displacement of 5 km. How many kilometers are represented by
a 3 cm vector drawn to the same scale?
3. What is the largest possible displacement resulting from two displacements with magnitudes 10 m and 25
m? What is the smallest possible resultant? Draw sketches to illustrate your answers.
4. Is the distance you walk equal to the magnitude of your displacement? Give an example that supports your
conclusion.
5. True or false, and give an example for your answer: A vector quantity always has to be a distance.
Drawing Vectors - For each vector, select a scale and draw the vector to that scale. Be sure to label both the
magnitude and the direction of the vector, and the scale for each vector.
6.
7.
8.
9.
10 m/s at 81º
30 N at 200º
12 mi/hr at 195º
20 N at 160º
Vector Addition
10. A hiker hikes 11 km north, and then 11 km east. What is the hiker’s displacement in both magnitude and
direction? (15.6 km, 45º)
11. A car is driven 125 km due west, then 65 km due south. What is the magnitude of its displacement?
12. Joey rides his skateboard east at 10 m/s. The wind is blowing west at 7 m/s. What is Joey’s resultant
velocity?
Relative Velocities
13. You are riding in a bus moving slowly through heavy traffic at 4.0 m/s. You hurry to the front of the bus at
4.0 m/s relative to the bus. What is your speed relative to the street? (0 m/s relative to the street)
14. A motorboat heads due west at 11 m/s relative to the water across a river that flows due north at 5.0 m/s.
What is the velocity of the motorboat with respect to the shore? (12 m/s, 156 °)
15. An airplane flies due west at 185 km/h with respect to the air. There is a wind blowing at 85 km/h to the
east relative to the ground. What is the plane’s speed with respect to the ground? (100 km/h)
Vector Resolution
16. A hiker walks 14.7 km at an angle of 325º. Because he isn’t tired enough at the end of his hike, he decides to
calculate the east and south components of his walk. What are they? (12.04 km, 8.43 km)
17. Hank goes on a 5 mile run with Mrs. Jensen at an angle of 120º. Because he is a super genius, Mrs. Jensen
decides to calculate the north and west components of their run so that he can discuss the finer points with
Mrs. Jensen over dinner. What are they? (the components, not the Jensen’s)
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Grade Level Physics
Unit 2: Vectors
18. Consider the grid below with several marked locations. 1 grid = 1cm. Determine the direction of the
resultant displacement for a person who walks from
location ...
a. E to K:
b. J to K to F:
c. I to K to B:
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