Applied Mathematics 30
Unit 4 Review: Vectors
Name: ________________________
Date: _________________________
Part A: Multiple Choice [ 11 marks ]
Please choose the response that best completes the statement or answers the question.
Write your answers on the answer sheet provided.
1. The scale 1 cm = 80 km/h was used to draw the vector below. What does the vector
represent?
3.5cm
a)
b)
c)
d)
280 km/h [ northeast ]
80 km/h [ southwest ]
80 km/h [ northeast]
280 km/h [ southwest ]
r r
2. If u v
a)
b)
c)
d)
r
0 and u
5060 N
5060 N
5060 N
5060 N
[
[
[
[
r
5060 N [ 095° ], then what is the magnitude and direction of v ?
095° ]
185° ]
275° ]
360° ]
r
r
3. Jeremy drew a vector, v . He is now asked to draw a second vector, kv , that is to be
r
shorter than v and acting in the opposite direction. Which of the following is true about
the value of ‘k’?
a)
b)
c)
d)
k is between 0 and 1
k is between –1 and 0
k<0
k<1
Use the following diagram to answer questions #4-#5.
A
B
C
F
E
D
uuur uuur
4. The resultant vector of AB BE is
a)
b)
c)
d)
uuur
EAr
uuu
AE
uuu
r
FB
uuur
BF
uuur uuur
5. The resultant vector of CA CD is
a)
b)
c)
d)
uuur
FC
uuur
CF
uuur
CE
uuur
EC
6. Jim decides to swim across a river that flows at 1.8 m/s toward the south. If Jim swims
at 1.3m/s toward the west, what is his resultant velocity?
a)
b)
c)
d)
2.2 m/s W 36° S
2.2 m/s S 54° W
2.2 m/s on a bearing of 36°
2.2 m/s on a bearing of 216°
7. An aircraft is flying on a bearing of 300° with an airspeed of 600 km/hr. It is being
affected by a 120 km/h wind blowing from the east, (going West). Draw the diagram.
The distance that the plane has travelled after one hour, to the nearest km, is
a)
b)
c)
d)
706 km
632 km
612 km
500 km
8. Two people are trying to raise an object from a hole using two ropes. Max exerts a force
of 375 N [250] and George exerts a force of 450 N [085]. Find the total amount of
resultant force applied by both Max and George and in what direction.
9. Karen and Dirk just received a box of Christmas presents from their parents who live in
Ontario. They are pushing the large box across a smooth floor so that they can sit it
next to the Christmas tree. If Karen pushes with a force of 60 N toward the southwest
and Dirk pushes with a force of 52 N toward the northwest, the resultant force is
a)
b)
c)
d)
112 N toward 229.1°
112 N toward 220.9°
79.4 N toward 274.1°
79.4 N toward 265.9°
10. Two construction workers are preparing to move a beam into position. They have a crane
to help them. The crane lifts up with a force of 2000 N. Each worker pulls with a force
of 750 N. One worker pulls east, the other south. The net force that acts on the beam
is
a)
b)
c)
d)
2750 N
2264 N
2136 N
1061 N
Part B: Numerical Response [ 5 marks ]
Write your answers on the answer sheet provided.
Use the following information to answer questions #1-#2.
A balloonist flying his ship north with an airspeed
of 150 km/h encounters a 45 km/h wind blowing towards the east.
1. To the nearest km/h, the resultant speed of the balloon, is ____________.
2. To the nearest degree, the true heading of the flight [ in bearings from North ], is
____________.
Use the following information to answer questions #3-#4.
A ship is travelling in the open seas with a speed of 50 knots [ nautical miles per hour ]
on a bearing of [042] and is being affected by a 12 knot current going east.
3. The ship’s actual velocity, to the nearest tenth of a knot, is ____________.
4. The ship’s direction, to the nearest tenth of a degree is N __________E.
5. A small plane is flying 180 km/h toward North. It is affected by a 20 km/h wind blowing
toward South. The actual speed of the plane is __________ km/h.
Applied Mathematics 30 Answer Sheet
Unit 4 Review: Vectors
Name: ________________________
Date: _________________________
Part A: Multiple Choice [ 11 marks ]
1. _______
2. _______
3. _______
4. _______
5. _______
6. _______
7. _______
8. _______
9. _______
10. _______
11. _______
Part B: Numerical Response [ 5 marks ]
1. __________
2. __________
4. __________
5. __________
3. __________
Part C: Written Response [ 6 marks ]
1. Two children are pulling a wagon. Each child exerts a force of 150 N. Each child is pulling
in a direction that is 35 away from the direction of travel, as shown below.
The force exerted by the children can be modeled by the vector diagram shown below.
150N
x
150N
a) Determine the measure of angle
in the vector diagram. [1 mark]
b) Calculate the magnitude, x , correct to the nearest tenth, of the resultant force
that the children exert on the wagon. [1 mark]
c) If a force of 250 N is required to move the wagon, will the children be able to do
so? Explain and justify your answer mathematically. [1 mark]
2. An airplane with an airspeed of 230 km/h leaves Grande Prairie on a bearing of 110 . It
is being affected by a 40 km/h wind blowing toward 70 .
a) Draw the vector diagram sketch for this situation on the axes below [ 1 mark ]
Vector Sketch
b) What is the resultant velocity of the airplane? Round to the nearest tenth. [ 1 mark ]
c) What is the resultant direction of the airplane, in the form E _____ o S ? Round to
the nearest tenth. [ 1 mark ]