Name: 
 

Trig Smig



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 
 
Instructions: On occasion, the notation nar001-1.jpg = [A, θ] will be a shorthand notation for nar001-2.jpg.
 

 1. 

If mc001-1.jpg = [15, 80°] and mc001-2.jpg, what is the magnitude of mc001-3.jpg?
a.
15
b.
35
c.
32
d.
5.0
e.
23
 

 2. 

Vectors mc002-1.jpg and mc002-2.jpg are shown. What is the magnitude of a vector mc002-3.jpg if mc002-4.jpg?

mc002-5.jpg
a.
46
b.
10
c.
30
d.
78
e.
90
 

 3. 

If mc003-1.jpg and mc003-2.jpg, what is the magnitude of the vector mc003-3.jpg?
a.
42
b.
22
c.
64
d.
90
e.
13
 

 4. 

If mc004-1.jpg = [10 m, 30°] and mc004-2.jpg = [25 m, 130°], what is the magnitude of the sum of these two vectors?
a.
20 m
b.
35 m
c.
15 m
d.
25 m
e.
50 m
 

 5. 

A vector, mc005-1.jpg, when added to the vector mc005-2.jpg yields a resultant vector which is in the positive y direction and has a magnitude equal to that of mc005-3.jpg. What is the magnitude of mc005-4.jpg?
a.
3.2
b.
6.3
c.
9.5
d.
18
e.
5
 

 6. 

If vector mc006-1.jpg is added to vector mc006-2.jpg, the result is mc006-3.jpg. If mc006-4.jpg is subtracted from mc006-5.jpg, the result is mc006-6.jpg. What is the direction of mc006-7.jpg (to the nearest degree)?
a.
225°
b.
221°
c.
230°
d.
236°
e.
206°
 

 7. 

If two collinear vectors mc007-1.jpg and mc007-2.jpg are added, the resultant has a magnitude equal to 4.0. If mc007-3.jpg is subtracted from mc007-4.jpg, the resultant has a magnitude equal to 8.0. What is the magnitude of mc007-5.jpg?
a.
2.0
b.
3.0
c.
4.0
d.
5.0
e.
6.0
 

 8. 

Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What distance separates the two oases?
a.
15 km
b.
48 km
c.
28 km
d.
53 km
e.
55 km
 

 9. 

The three forces shown act on a particle. What is the magnitude of the resultant of these three forces?

mc009-1.jpg
a.
27.0 N
b.
33.2 N
c.
36.3 N
d.
23.8 N
e.
105 N
 

 10. 

A student decides to spend spring break by driving 50 miles due east, then 50 miles 30 degrees south of east, then 50 miles 30 degrees south of that direction, and to continue to drive 50 miles deviating by 30 degrees each time until he returns to his original position. How far will he drive, and how many vectors must he sum to calculate his displacement?
a.
0, 0
b.
0, 8
c.
0, 12
d.
400 mi, 8
e.
600 mi, 12
 

 11. 

Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity?
a.
14 km/h, E
b.
14 km/h, W
c.
14 km/h, N
d.
90 km/h, S
e.
90 km/h, N
 

 12. 

The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true?

mc012-1.jpg
a.
mc012-2.jpg
b.
mc012-3.jpg
c.
mc012-4.jpg
d.
mc012-5.jpg
e.
mc012-6.jpg
 

 13. 

Vectors mc013-1.jpg and mc013-2.jpg have equal magnitudes. Which statement is always true?
a.
mc013-3.jpg.
b.
mc013-4.jpg.
c.
mc013-5.jpg is perpendicular to mc013-6.jpg.
d.
mc013-7.jpg is perpendicular to mc013-8.jpg.
e.
The magnitude of mc013-9.jpg equals the magnitude of mc013-10.jpg.
 

 14. 

When three vectors, mc014-1.jpg, mc014-2.jpg, and mc014-3.jpg are placed head to tail, the vector sum mc014-4.jpg. If the vectors all have the same magnitude, the angle between the directions of any two adjacent vectors is
a.
30°
b.
60°
c.
90°
d.
120°
e.
150°
 

 15. 

The vectors mc015-1.jpg, mc015-2.jpg, and mc015-3.jpg are shown below.

mc015-4.jpg

Which diagram below correctly represents mc015-5.jpg?
a.
mc015-6.jpg
c.
mc015-8.jpg
e.
mc015-10.jpg
b.
mc015-7.jpg
d.
mc015-9.jpg
 

 16. 

The vectors mc016-1.jpg, mc016-2.jpg, and mc016-3.jpg are shown below.

mc016-4.jpg

Which diagram below correctly represents mc016-5.jpg?
a.
mc016-6.jpg
c.
mc016-8.jpg
e.
mc016-10.jpg
b.
mc016-7.jpg
d.
mc016-9.jpg
 

 17. 

The diagram below shows the path taken by a sailboat tacking sideways because it cannot sail directly into the wind.

mc017-1.jpg

The total distance it travels is
a.
1 000 m.
b.
1 732 m.
c.
2 000 m.
d.
6 298 m.
e.
8 000 m.
 

 18. 

The vector mc018-1.jpg has components +5 and +7 along the x- and y-axes respectively. Along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are
a.
7; 5.
b.
7; 5.
c.
7; 5.
d.
7; 5.
e.
7; 0.
 

 19. 

Anthony has added the vectors listed below and gotten the result mc019-1.jpg. What errors has he made?

     mc019-2.jpg
     mc019-3.jpg
     mc019-4.jpg
a.
He lost the minus sign in vector mc019-5.jpg.
b.
He read the mc019-6.jpg in mc019-7.jpg as mc019-8.jpg.
c.
He lost the minus sign in vector mc019-9.jpg.
d.
All of the above are correct.
e.
Only (a) and (b) above are correct.
 

 20. 

Given the statement that mc020-1.jpg, what can we conclude?
a.
mc020-2.jpg and mc020-3.jpg.
b.
mc020-4.jpg.
c.
mc020-5.jpg and mc020-6.jpg.
d.
Any one of the answers above is correct.
e.
Only (a) and (b) may be correct.
 



 
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