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Learning Vectors Practice
Question 1:
What is the scale of this vector?
60 km/h
c) 1 cm = 15 km/h
Centimers (cm)
d) I have no idea
Learning Vectors Practice
Question 2:
An airplane travels north. A tailwind also blows
north. Will the velocity of the plane be:
d) I have no idea
Learning Vectors Practice
Question 3:
the
plane traveling relative to the ground?
d) I have no idea
Learning Vectors Practice
Question 4:
relative to the ground with a headwind?
Learning Vectors Practice
Question 5:
est. Will the wind cause the planes velocity to:
Learning Vectors Practice
Question 6:
Suppose our plane is flying at 40 km/hr north, and
encounters a wind blowing at 30 km/hr from the
west. What is the plane's speed?
a) 50 km/hr
b) 60 km/h
c) 70 km/h
a
b
b
= 2500 km
Learning Vectors Practice
100 km
Question 7:
100 km
= 190 km
Learning Vectors Practice
Question 8:
100 km
How far is he from where he started?
(50 km)
(40 km)
64km
Learning Vectors Practice
Start
the Tip-to-Tail
Method, the
always be the
same!
Learning Vectors Practice
Start
the Tip-to-Tail
Method, the
always be the
same!
c = √(160.0 N) + (90.0 N)
c = √25600 N + 8100 N
Learning Vectors Practice
Question 10:
Re-draw using the tip-to-tail method and determine
the missing vector(s)'s magnitude and direction.
220 m/s
220 m/s
c = √(220 m/s)2 + (220 m/s)2
or c = √2(220 m/s)2
c = √96800 m2/s2
c = 311 m/s
A. Determine the resultant vector.
160.0 N
90.0 N
c = √(160.0 N)2 + (90.0 N)2
c = √25600 N2 + 8100 N2
c = √33700 N2
c = 184 N
B. Determine the resultant vector.
c2 = a2 + b2
- b2
65
0m
?
- b2
c 2 - b2 = a 2
√c2 - b2 = a
√(650 m)2 - (520 m)2 = a
√422500 m2 - 270400 m2 = a
520 m
√152100 m2 = a
390 m = a
C. Determine the missing (?) component.
a2 + b2 = c2 ==> a2 + a2 = c2
?
?
0
10
2a2 = c2
/s
m
D. Determine the missing (?)
components.
NOTE: Think about what kind of
triangle this is.
2
2
√a2 = √(c2/2)
Since this is a perfect square
(45o-45o-90o triangle) both
sides will have the same
magnitude.
a = √(c2/2)
a = √(100 m/s)2/2)
a = √(10000 m2/s2)/2)
a = √5000 m/s
a = 71 m/s
Learning Vectors Practice
1. You walk 5 km to the south and then 3 km 45° west of south. What is
your final displacement?
5 km
a
a
a
a
a
?
a
√(c2/2)
√(32/2)
√9/2
√4.5
2.12 km
3
km
a
=
=
=
=
=
√a2 + b2 = c
√(7.12)2 + (2.12)2 = c
√50.6944 + 4.4944 = c
√55.1888 = c
7.428916476 = c
5 km
2.12 km
7.4 km SW
2.12 km
m
150 m/s
a
a
?
a
a
a
a
a
=
=
=
=
=
√(c2/2)
√(502/2)
√2500/2
√1250
35.36 km
150 m/s
0
5
35.36 m/s
2. An airplane is flying at 150 m/s to the north. The wind is blowing in a
direction 45° east of north at 50 m/s. What is the resulting velocity of the
35.36 m/s
plane?
/s
√a2 + b2 = c
√(185.36)2 + (35.36)2 = c
√34358.3296 +1250.3296 = c
√35608.6592 = c
188.7025681 = c
190 m/s NE
N
a
a
115 N
?
a
a
a
a
a
=
=
=
=
=
√(c2/2)
√(1102/2)
√12100/2
√6050
77.78 N
115 N
0
11
77.78 N
3. Two people pull a wagon using two ropes with an angle of 45o between
them. If one person pulls with 110N and the other with 115 N, what is the
resulting force on the wagon?
77.78 N
√a2 + b2 = c
√(192.78)2 + (77.78)2 = c
√37164.1284 +6049.7284 = c
√43213.8568 = c
207.8794285 = c
208 N NE
4. A soccer player runs forward a distance of 4 m, reverses direction and
runs a distance of 3 m, and then reverses direction again and runs a
distance of 8 m.
a. What distance does the player run?
b. What is his displacement?
4m
3m
8m
4m
8m
3m
a.
15 m
b.
4m
8m
3m
12 m
9 m FORWARD
Learning Vectors Practice
0.24 km N
5. A jogger starts a three-part jog by running 0.24 km north, then 0.16 km
east, and finally back to her starting point along a straight-line path.
Graphically determine the jogger’s third displacement.
0.16 km E
√a2 + b2 = c
√(0.24) + (0.16)2 = c
√0.0576 + 0.0256 = c
√0.0832 = c
0.288444102 = c
2
0.29 km NE
4.0 m Forward(right)
6.0 m Left
3.0 m up
6. A gymnast tumbles forward 4.0 m, does cartwheels to the left for 6.0 m,
and climbs a vertical rope to a height of 3.0 m. What is the magnitude of
the gymnast’s displacement?
2.0 m Left
2.0 m Left
√a2 + b2 = c
√(2.0)2 + (3.0)2 = c
√4 + 9 = c
√13 = c
3.605551275 = c
3.6 m up and to the left
7. The moving sidewalk at an airport has a speed of 0.9 m/s toward the
departure gate. A man is walking toward the departure gate on the moving
sidewalk at a speed of 1.0 m/s relative to the sidewalk.
- What is the velocity of the man relative to a woman standing off the
moving sidewalk.
0.9 m/s towards gate
1.0 m/s towards gate
0.9 m/s towards gate
1.0 m/s towards gate
1.9 m/s towards gate
– On a similar moving sidewalk moving in the opposite direction, a child
walks toward the terminal at a speed of 0.4 m/s relative to the
sidewalk. What is the velocity of the man relative to the child?
0.4 m/s towards terminal
0.4 m/s towards terminal
0.9 m/s towards terminal
1.9 m/s towards gate (man)
1.3 m/s towards terminal (child)
0.6 m/s towards gate
Learning Vectors Practice
8. A hiker starts by walking along a straight path. He then turns and walks
260.0 m west. If he finds he is located 360.0 m exactly north of his starting
point, what was his displacement along the path?
260.0 m W
360.0 m N
?
√a2 + b2 = c
√(260.0)2 + (360.0)2 = c
√67600 + 129600 = c
√197200 = c
444.0720662 = c
444.1 m NW
9. Two teams pull on a rope in a tug of war competition. Team A pulls with
a force of 2340 N while Team B pulls with a force of 3000 N. Draw a vector
diagram of the situation and determine the resultant force.
3000 N
2340 N
3000 N
2340 N
660 N
towards Team B
10.Iggy pulls a toy wagon with a horizontal force of 80 N and he pulls at an
angle of 45 degrees from the horizontal.
> Determine the actual (resultant) force Iggy applies to the handle as
he pulls.
> Determine the vertical force applied by Iggy?80 N, since this is 45-45-90 triangle
√2a2 = c
√2(80 N)2 = c
80 N
√2(6400 N)2 = c
√12800 = c
113.137085 = c
113 N at 45o
both the vertical and horizontal
components have the same
magnitude.
Learning Vectors Practice
11.Juniper shoots an arrow at an apple 10 meters above her in a tree. She
shoots at an angle of 45 degrees. Determine the horizontal and vertical
velocities of the arrow if the resultant velocity was 80 m/s.
a = √(c2/2)
a = √(802/2)
a = √6400/2
a = √3200
a = 56.56854249
57 m/s for both the vertical and horizontal components
/s
m
80
45o
12.Bonzi rows a boat at a speed of 0.5 m/s across a river and in a direction
perpendicular to the shore. If the river is flowing at 2.5 m/s, at what
velocity will the boat go as it crosses the river?
2.5 m/s
√a2 + b2 = c
√(2.5)2 + (0.5)2 = c
√6.25 + 0.25 = c
√6.5 = c
2.549509757 = c
0.5 m/s
3 m/s NE
13.Determine the displacement between the start and end points. You
start at the tree and go 20 paces north, then 15 paces west, then 30 paces
south, then 10 paces east, then 40 paces 45 degrees north of east, then 20
paces south and 20 paces west.
First find the components of the 40 paces at 45o NE.
a
a
a
a
a
N
E
15 W
40
40
√(c2/2)
√(402/2)
√1600/2
√800
28.28427125
28 paces for both the north and east
components
20 S
NE
30 S
20 N
=
=
=
=
=
20 W
10 E
15 W
Next, using the NE vertical component,
find all the vertical displacement.
2S
Then using the NE horizontal component,
find all the horizontal displacement.
20 S
3W
2S
Lastly, use the total vertical component
and the total horizontal component, to
find the total displacement.
3W
√a2 + b2 = c
√(2)2 + (3)2 = c
√4 + 9 = c
√13 = c
3.605551275 = c
4 paces SW
20 N
35 W
38 E
50 S
48 N
38 E
48 N
28 E
28 N
10 E
30 S
35 W
50 S
20 W