151: Physics Vector Mathematics
r 1) The vector A is: v A) greater than A in magnitude r C) in the direction opposite to A
v B) less than A in magnitude r D) perpendicular to A
2) Select the list which contains only vector quantities? A) distance, force, power, energy B) velocity, force, acceleration, displacement C) mass, volume, acceleration, work D) current, temperature, velocity, force
r r r r r r 3) The vectors a , b , and c are related by c = b a . Which diagram below illustrates this relationship?
A) A
B) B
C) C
D) D
r 4) The vector V 3 in the diagram is equal to:
r r A) V 1 V 2
r r B) V 1 + V 2
r r C) V 2 V 1
r D) V 1 cos
5) A vector of magnitude 3 CANNOT be added to a vector of magnitude 4 so that the magnitude of the resultant is: A) zero B) 1 C) 5 D) 7 6) Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the sum A) is 2.0 m. B) could be as small as 2.0 m, or as large as 12 m. C) is 12 m. D) is larger than 12 m. 7) Which of the following is an accurate statement? A) A vector cannot have zero magnitude if one of its components is not zero. B) The magnitude of a vector can be less than the magnitude of one of its components. C) If the magnitude of vector A is less than the magnitude of vector B, then the xcomponent of A is less than the x-component of B. D) The magnitude of a vector can be positive or negative.
8) The resultant of two vectors is the smallest when the angle between them is: A) 0 B) 45 C) 90 D) 180 9) A vector in the xy plane has a magnitude of 25 m and an x component of 12 m. The angle it makes with the positive x axis is: A) 26 B) 29 C) 61 D) 64 E) 241 10) TRUE or FALSE: Can or three more vectors with unequal magnitudes be added together so their sum is zero? 11) What is the minimum number of vectors with equal magnitudes whose vector sum is zero? A) two B) three C) four D) five E) Six 12) The x and y components of a displacement vector are -3.00 m and 4.00 m respectively. What angle does this vector make with the positive x axis? A) 233 B) 127 C) -53 D) 53 E) 37 13) If a ball is thrown with a velocity of 25 m/s at an angle of 37 above the horizontal, what is the vertical component of the velocity? A) 12 m/s B) 15 m/s C) 19 m/s D) 25 m/s 14) If you walk 6.0 km in a straight line in a direction north of east and you end up 2.0 km north and several kilometers east. How many degrees north of east have you walked? A) 19 B) 45 C) 60 D) 71 15) A butterfly moves with a speed of 12.0 m/s. The x component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x axis must be A) 30.0. B) 41.8. C) 48.2. D) 53.0. 16) A 400-m tall tower casts a 600-m long shadow over a level ground. At what angle is the Sun elevated above the horizon? A) 34 B) 42 C) 48 D) can't be found; not enough info. 17) Two vectors A and B have components (0, 1) and (-1, 3), respectively. What is magnitude of the sum of these two vectors? A) 2.8 B) 3.2 C) 3.9 D) 4.1 18) Two vectors, of magnitudes 20 and 50, are added. Which one of the following is a possible answer for the magnitude of the resultant? A) 10 B) 20 C) 40 D) 80 19) A car travels 20 km west, then 20 km south. What is the magnitude of its displacement? A) 0 km B) 20 km C) 28 km D) 40 km 20) If vector A = (-3.0, -4.0) and vector B = (+3.0, -8.0), what is the magnitude of vector C = A - B? A) 13 B) 16 C) 144 D) 7.2