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HOMEWORK 3 - VECTORS - HON
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1.
What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?
a. two
b. three
c. four
d. five
e. six
____
2.
What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?
a. two
b. three
c. four
d. five
e. six
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3.
⃗⃗ are added together to form a vector 𝐶⃗ . The relationship between the magnitudes of the vectors is
Two vectors 𝐴⃗ and 𝐵
given by A + B = C. Which one of the following statements concerning these vectors is true?
⃗⃗ must be displacements.
a. 𝐴⃗ and 𝐵
⃗⃗ must have equal lengths.
b. 𝐴⃗ and 𝐵
⃗⃗ must point in opposite directions.
c. 𝐴⃗ and 𝐵
⃗⃗ must point in the same direction.
d. 𝐴⃗ and 𝐵
⃗⃗ must be at right angles to each other.
e. 𝐴⃗ and 𝐵
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4.
What is the angle between the vectors 𝐴⃗ and – 𝐴⃗ when they are drawn from a common origin?
a. 0°
b. 90°
c. 180°
d. 270°
e. 360°
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5.
Which expression is false concerning the vectors shown in the sketch?
a.
b.
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6.
=
+
+
=–
c.
d.
+
C<A+B
+
=0
e.
A2+B2=C2
A jet moving at 500.0 km/h due east moves into a region where the wind is blowing at 120.0 km/h in a direction 30.0 0
of east. What is the new velocity and direction of the aircraft relative to the ground?
a. 607 km/h, 5.670 north of east
c. 550.0 km/h, 6.220 north of east
0
b. 620.0 km/h, 7.10 north of east
d. 588 km/h, 4.870 north of east
north
2
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7.
A boat is able to move through still water at 20 m/s. It makes a round trip to a town 3.0 km downstream. If the river flows at 5
m/s, the time required for this round trip is:
a. 120 s
b. 150 s
c. 200 s
d. 300 s
e. 320 s
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9.
An airplane makes a gradual 900
turn while flying at a constant speed of 200 m/s. The process takes 20.0 seconds to
⃗⃗ −𝑣
⃗⃗
𝑣
complete. For this turn the magnitude of the average acceleration of the plane is: 𝑎⃗ = 2 1
𝑡
a.
zero
b.
40 m/s2 c.
20 m/s2 d.
14 m/s2 e.
10 m/s2
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11. A body is acted upon by the two forces shown. In each case draw the one force whose effect on the body is the same as the
two together.
12. A person walks 5.0 km due east, then 3.0 km due north and finally stops after walking an additional 2.0 km due north-east. How
far and in what direction relative to her starting point is she?
13. A person walks 5 km east, followed by 3 km north and then another 4 km east. Where does he end up?
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14. The displacement vector of a moving object has components (rx = 2, ry = 2) initially. After a certain time the displacement vector
has components (rx = 4, ry = 8). What vector represents the change in the displacement vector ( ∆𝑟⃗ = 𝑟⃗2 − 𝑟⃗1 )?
15. In physics we are often interested in finding the change in a vector. For example, consider a body whose velocity changes from
to
. Find vector representing the change in the velocity
.
16. Figure shows the velocity vector of a particle moving in a circle with speed 10 m/s at two separate points. The velocity vector
is tangential to the circle. Find the vector representing the change in the velocity vector.
17. A molecule with a velocity of 352 m/s collides with a wall as shown and bounces back with the same speed.
(a) What is the change in the molecule’s velocity?
(b) What is the change in the speed?
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18. A body moves in a circle of radius 3 m with a constant speed of 6.0 m/s. The velocity vector is at all times tangent to the circle.
The body starts at A and proceeds to B and then C. Find the change in the velocity vector between A and B and between B and
C.
19. Find the magnitude and direction of the vectors with components:
(a)
Ax = —4.0 cm,
(b)
Ax = 124 km,
Ay =
(c)
Ax = 0,
—5.0 m
(d)
Ax = 8 N,
Ay =
Ay =
—4.0 cm
-158 km
Ay = 0.
20. A velocity vector of magnitude 1.2 m/s is horizontal. A second velocity vector of magnitude 2 m/s must he added to the first so
that the sum is vertical in direction. What is the direction of the second vector and what is the magnitude of the sum?
21.
,
. Find the magnitude of
and
and magnitude of
.
22. Find vector
(magnitude and direction) if
and
.
23. Find vector
(magnitude and direction) if
and
.
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24. Vector
has a magnitude of 12 units and makes an angle of 300 with the positive x-axis. Vector
has a magnitude of 8
units and makes an angle of 800 with the positive x-axis. Sketch and calculate the magnitude and directions of the vectors
(a)
(b)
25. Vectors
and
(c)
have components:
(Ax = 3, Ay = 4), (Bx = —1, By = 5). Find the magnitude and direction of the
vector
such that
26. Lynn is driving home from work and finds that there is road construction being done on her favorite route, so she must take a
detour. Lynn travels 5 km north, 6 km east, 3 km south, 4 km west, and 2 km south. a) Draw a vector diagram of the situation.
b) What is her displacement? Solve graphically.
c) What total distance has Lynn covered?
27.
Avery sees a UFO out her bedroom window and calls to report it to the police. She says, “The UFO moved 20.0 m east, 10.0 m
north, and 30.0 m west before it disappeared.” What was the displacement (how far and in what direction are they from
original position) of the UFO while Avery was watching? Solve graphically and numerically.
28.
Eli finds a map for a buried treasure. It tells him to begin at the old oak and walk 21 paces due west, 41 paces at an angle 45°
south of west, 69 paces due north, 20 paces due east, and 50 paces at an angle of 53° south of east. How far from the oak tree
is the buried treasure? Solve graphically.
29.
Ralph is mowing the back yard with a push mower that he pushes downward with a force of 20.0 N at an angle of 30.00 to the
horizontal. What are the horizontal and vertical components of the force exerted by Ralph?
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30.
Dwight pulls his sister in her wagon with a force of 65 N at an angle of 50.0° to the vertical. What are the horizontal and vertical
components of the force exerted by Dwight?
31.
Erica and Tory are out fishing on the lake on a hot summer day when they both decide to go for a swim. Erica dives off the front
of the boat with a force of 45 N, while Tory dives off the back with a force of 60. N.
a) Draw a vector diagram of the situation. b) Find the resultant force on the boat.
32.
Shareen finds that when she drives her motorboat upstream she can travel with a speed of only 8 m/s, while she moves with a
speed of 12 m/s when she heads downstream. What is the current of the river on which Shareen is traveling?
33.
Rochelle is flying to New York for her big Broadway debut. If the plane heads out of Los Angeles with a velocity of 220. m/s in a
northeast direction, relative to the ground, and encounters a wind blowing head-on at 45 m/s, what is the resultant velocity of
the plane, relative to the ground?
34.
In Moncton, New Brunswick, each high tide in the Bay of Fundy produces a large surge of water known as a tidal bore. If a
riverbed fills with this flowing water that travels north with a speed of 1.0 m/s, what is the resultant velocity of a puffin who
tries to swim east across the tidal bore with a speed of 4.0 m/s?
35.
Veronica can swim 3.0 m/s in still water. While trying to swim directly across a river from west to east, Veronica is pulled by a
current flowing southward at 2.0 m/s. a) What is the magnitude of Veronica’s resultant velocity? b) If Veronica wants to end up
exactly across stream from where she began, at what angle to the shore must she swim upstream?
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HOMEWORK - VECTORS 3
1. B
2.A
3.D
4.C
5.A
6.A
7.E
8.B
9.D
10.E
11.
12. 7.79 km @ 34.50
13. OC = OA + AB + BC
as vectors
OCx = OAx + ABx + BCx = 5 + 0 + 4 = 9 km
OCy = OAy + ABy + BCy = 0 + 3 + 0 = 3 km
 = arc tan ( 3/9) = 18.40
OC = 9.5 km @ 18.40
14. (2, 6)
15.
16.
17. (a) 704 m/s in magnitude
18. a.
vector
b.
vector
From A to B we have to find the difference
= 8.49 m/s, south - west (S - W)
From B to C we have to find the difference
= 8.49 m/s, north - west (N
19. (a)
(c)
.
(b)
(d)
- W)
.
(b) zero
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v  v1  v 2
20.
=?
v=?
v 1 = 1.2 m/s, east
v2 = 2 m/s , 
vx = 0
vy = v
two equations with two unkowns v and 
vx = v1x + v2x = 1.2 cos 00 + 2 cos 
vy = v1y + v2y = 1.2 sin 00 + 2 sin 

0 = 1.2 + 2 cos  v =2 sin 
 1.6 m/s
21.
22.
so the magnitude is 2.
23.
24. (a)
25.
.
27. 14.1 m
(b)
(c)
.
26
450 north of west
28. Solving graphically brings Eli back
to the starting point.
29. Horizontal component:
 = (20.0 N) cos (-300) = 17.3 N
Fy = F sin  = (20.0 N) sin (-300) = -10.0 N
Fx = F cos
Vertical component:
30. horizontal component: Fx = F cos  = (65 N) cos 400 = 50. N
vertical component:
Fy = F sin  = (65 N) sin 400 = 42 N
31. b. 60. N - 45 N = 15 N forward
32. 12 m/s – v = 8 m/s + v
v = 2 m/s downstream
33. 220. m/s – 45 m/s = 175 m/s to the northeast
2
2
34. v  (1.0 m / s )  ( 4.0 m / s )
35. v = 3.6 m/s
= 420
v = 4.1 m/s
tan  = (4.0 m/s)/(1.0m/s)
760 east of north