Multiple Choice Identify the choice that best completes the
statement or answers the question.
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Instructions: On occasion, the notation = [ A,
θ] will be a shorthand notation for .
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1.
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If = [15, 80 °]
and , what is the magnitude of ?
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2.
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Vectors and are shown. What is the magnitude of a
vector if ?
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3.
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If and , what is the magnitude of the vector
?
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4.
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If = [10 m, 30 °]
and = [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 |
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5.
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A vector, , when added to the vector yields a resultant
vector which is in the positive y direction and has a magnitude equal to that of .
What is the magnitude of ?
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6.
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If vector is added to vector , the result is .
If is subtracted from , the result is . What is the direction
of (to the nearest degree)?
a. | 225° | b. | 221° | c. | 230° | d. | 236° | e. | 206° |
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7.
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If two collinear vectors and are added, the
resultant has a magnitude equal to 4.0. If is subtracted from , the
resultant has a magnitude equal to 8.0. What is the magnitude of ?
a. | 2.0 | b. | 3.0 | c. | 4.0 | d. | 5.0 | e. | 6.0 |
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8.
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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 |
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9.
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The three forces shown act on a particle. What is the magnitude of the resultant
of these three forces?
a. | 27.0 N | b. | 33.2 N | c. | 36.3
N | d. | 23.8 N | e. | 105 N |
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10.
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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 |
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11.
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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 |
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12.
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The diagram below shows 3 vectors which sum to zero, all of equal length. Which
statement below is true?
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13.
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Vectors and have equal magnitudes. Which statement
is always true?
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14.
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When three vectors, , , and are placed head to
tail, the vector sum . 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° |
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15.
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The vectors , , and are shown
below. Which diagram below correctly represents ?
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16.
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The vectors , , and are shown
below. Which diagram below correctly represents ?
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17.
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The diagram below shows the path taken by a sailboat tacking sideways because it
cannot sail directly into the wind. 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. |
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18.
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The vector 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. |
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19.
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a. | He lost the minus sign in vector . | b. | He read the
in as . | c. | He lost the minus sign in vector . | d. | All of the above are correct. | e. | Only (a) and (b) above are
correct. |
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20.
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Given the statement that , what can we conclude?
a. | and . | b. | . | c. | and . | d. | Any one of the
answers above is correct. | e. | Only (a) and (b) may be
correct. |
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