Chapter 1& 2 (Speed, Velocity, Vectors)

1.  Which formula is dimensionally consistent with an expression yielding a value for velocity?  (a is acceleration, x is distance, and t is time)

            a. v/t²

            b. vx²

            c. v²/t

            d. at

2.  Since 1983 the standard meter has been defined in terms of which of the following?

            a. specific alloy bar housed at Sevres, France

            b. wavelength of light emitted by krypton‑86

            c. distance from the Earth’s equator to the north pole

            d. the distance light travels in 1/(3 ´ 10⁸) second

3.  Since 1967 the standard definition for the second has been based on which of the following?

            a. characteristic frequency of the cesium‑133 atom

            b. average solar day

            c. sidereal day

            d. Greenwich Civil Time

4.  On planet Q the standard unit of volume is called the guppy. Space travelers from Earth have determined that one liter = 38.2 guppies. How many guppies are in 150 liters?

            a. 5730 guppies

            b. 0.255 guppies

            c. 3.93 guppies

            d. 188 guppies

5.  Assume everyone in the United States consumes one soft drink in an aluminum can every two days. If there are 270 million Americans, how many tons of aluminum need to be recycled each year if each can weighs 1/16 pound and one ton = 2000 pounds?

            a. 750,000 tons

            b. 1.5 million tons

            c. 1.75 million tons

            d. 3 million tons

6.  Note the expression: y = x². Which statement is most consistent with this expression?

            a. if y doubles, then x quadruples

            b. y is greater than x

            c. if x doubles, then y doubles

            d. if x doubles, then y quadruples

7.  In mechanics, physicists use three basic quantities to derive additional quantities. Mass is one of the three quantities. What are the other two?

            a. length and force

            b. power and force

            c. length and time

            d. force and time

8.  Which formula is dimensionally consistent with an expression that would yield a value for time^-1 (v is velocity, x is distance, and t is time)?

            a. v/x

            b. v²/x

            c. x/t

            d. v²t

9.  Note the expression: y = A/x³. Which statement is most consistent with this expression?

            a. y is less than A

            b. if x is halved, y is multiplied by eight

            c. if x is doubled, y is multiplied by a factor of 8

            d. y is greater than x

10. On planet Z, the standard unit of length is the foose. Ann the Astronaut is 5.90 feet tall on earth. She lands on planet Z and is measured to be 94 foosi tall. Her partner Rachael is 88 foosi tall. How tall is Rachael on earth?

            a. 5.2 feet

            b. 5.5 feet

            c. 5.8 feet

            d. 6.3 feet

11. A furlong is a distance of 220 yards. A fortnight is a time period of 2 weeks. A race horse is running at a speed of 5 yards per second. What is his speed in furlongs per fortnight?

            a. 27,491 furlongs/fortnight

            b. 13,674 furlongs/fortnight

            c. 6,221 furlongs/fortnight

            d. 2,749 furlongs/fortnight

12. If the displacement of an object, x, is related to velocity, v, according to the relation x = Av, the constant, A, has the dimension of which of the following?

            a. acceleration

            b. length

            c. time

            d. area

13. A cereal box has the dimensions of 0.19 m ´ 0.28 m ´ 0.07 m. If there are 3.28 feet per meter, then what is the volume of the box in cubic feet?

            a. 0.13 cubic feet

            b. 0.22 cubic feet

            c. 0.49 cubic feet

            d. 1.3 cubic feet

14. A train slowly climbs a 500 m mountain track which is at an angle of 10˚ with respect to the horizontal. How much altitude does it gain?

            a. 87 m

            b. 123 m

            c. 341 m

            d. 492 m

15. The distance to the Andromeda Galaxy is estimated at about 2 ´ 10⁶ light years. A light year is the distance traveled by light in one year; if the speed of light is 3 ´ 10⁸ m/s, about how far is it from our galaxy to Andromeda? (1 year = 3.15 ´ 10⁷ s)

            a. 10 ´ 10¹⁵ m

            b. 1 ´ 10¹⁸ m

            c. 1.9 ´ 10²² m

            d. 6 ´ 10¹² m

16. Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 12.4 + 11 + 67.37 + 4.201?

            a. 94.971

            b. 94.97

            c. 95.0

            d. 95

17. Which one of the choices below represents the preferred practice regarding significant figures when multiplying the following: 10.5 ´ 8.8 ´ 3.14?

            a. 290

            b. 290.136

            c. 290.1

            d. 300

18. The speed of a boat is often given in knots. If a speed of 5 knots were expressed in the SI system of units, the units would be:

            a.. m

            b. s

            c. m/s

            d. kg/s

19. For which of the values below is x > x³?

            a. x = ‑1.5

            b. x = 0.5

            c. x = 1.0

            d. x = 1.5

20. If a is acceleration, v is velocity, x is position, and t is time, then which equation is not dimensionally correct?

            a. t = x/v

            b. a = v²/x

            c. v = a/t

            d. t² = 2x/a

21. A cement truck can pour 20 cubic yards of cement per hour. Express this in ft³/min.

            a. 1/3 ft³/min

            b. 1.0 ft³/min

            c. 3 ft³/min

            d. 9 ft³/min

22. Calculate (0.82 + 0.042) ´ (4.4 ´ 10³), keeping only significant figures.

            a. 3800

            b. 3784

            c. 3792

            d. 3520

23. Water flows into a swimming pool at the rate of 8 gal/min. The pool is 16 ft wide, 32 ft long and 8 ft deep. How long does it take to fill? (1 U.S. gallon = 231 cubic inches)

            a. 32 hours

            b. 64 hours

            c. 48 hours

            d. 24 hours

24.       

            a. S = 45

            b. S = 98

            c. S = 112

            d. S = 375

25. Which point is nearest the x‑axis?

            a. (-3,4)

            b. (4,5)

            c. (‑5,3)

            d. (5, -2)

26 Modern electroplaters can cover a surface area of 60 m² with one troy ounce of gold (volume = 1.611 cm³).What is the thickness of the electroplated gold?

            a. 2.68 ´ 10^‑8 m

            b. 1.34 ´ 10^‑9 m

            c. 1.67 ´ 10^-6 m

            d. 3.33 ´ 10^‑7 m

27. A high fountain of water is in the center of a circular pool of water. You walk the circumference of the pool and measure it to be 150 meters. You then stand at the edge of the pool and use a protractor to gauge the angle of elevation of the top of the fountain. It is 55˚. How high is the fountain?

28. When NASA was communicating with astronauts on the moon, the time from sending to receiving was 1.28 s. Find the distance from Earth to the moon. (The speed of radio waves is 3 ´ 10⁸ m/s).

            a. 240,000 km

            b. 384,000 km

            c. 480,000 km

            d. 768,000 km

29. The mass of the sun is 2 ´ 10³⁰ kg, and the mass of a hydrogen atom, of which the sun is mostly composed, is 1.67 ´ 10^‑27 kg. How many atoms are there in the sun?

            a. 1.2 ´ 10⁵⁶ atoms

            b. 3.4 ´ 10⁵⁶ atoms

            c. 1.2 ´ 10⁵⁷ atoms

            d. 2.4 ´ 10⁵⁷ atoms

30. The basic function of an automobile’s carburetor is to atomize the gasoline and mix it with air to promote rapid combustion. Assume that 30 cm³ of gasoline is atomized into N spherical droplets. Each droplet has a radius of 2.0 ´ 10^‑5 m. Find the total surface area of these N spherical droplets.

            a. 2,140 cm²

            b. 10,140 cm²

            c. 21,400 cm²

            d. 44,770 cm²

Ch 2   (Additional Q’s)

Vectors:

V1.       Which type of quantity is characterized by both magnitude and direction?

a. scalar

b. vector

c. trigonometric

d. algebraic variable

V2.       In a 2‑dimensional Cartesian coordinate system the x‑component of a given vector is equal to that vector’s magnitude multiplied by which trigonometric function, with respect to the angle between vector and x‑axis?

a. sine

b. cosine

c. tangent

d. cotangent

V3.    Which of the following is an example of a vector quantity?

a. velocity

b. temperature

c. volume

d. mass

V4.       In a 2‑dimensional Cartesian coordinate system the y‑component of a given vector is equal to that vector’s magnitude multiplied by which trigonometric function, with respect to the angle between vector and yaxis?

a. sine

b. cosine

c. tangent

d. cotangent

V5.       When we subtract a velocity vector from another velocity vector, the result is:

a. another velocity

b. an acceleration

c. a displacement

d. a scalar

V6.       When we add a displacement vector to another displacement vector, the result is:

a. a velocity

b. an acceleration

c. another displacement

d. a scalar

V7.     In a 2‑dimensional Cartesian system, the x‑component of a vector is known, and the angle between vector and x‑axis is known.  Which operation is used to calculate the magnitude of the vector (taken with respect to the x‑component?)

a. dividing by cosine

b. dividing by sine

c. multiplying by cosine

d. multiplying by sine

V8.       A taxicab moves five blocks due north, five blocks due east and another two blocks due north. Assume all blocks are of equal size. What is the magnitude of the taxi’s displacement, start to finish?

a. 12 blocks

b. 9.8 blocks

c. 9.2 blocks

d. 8.6 blocks

V9.       The following force vectors act on an object: i) 50 Newtons at 45˚ north of east and ii) 25 Newtons at 30˚ south of east. Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction?

            a. 75.0 Newtons 7.50˚

            b. 61.4 Newtons 21.8˚

            c. 23.4 Newtons 18.3˚

            d. 12.8 Newtons 37.5˚

V10.     Find the resultant of the following two vectors: i) 50 units due east and ii) 100 units 30˚ north of west.

a. 100 units 30˚ north of west

b. 116 units 15˚ north of west

c. 87 units 60˚ north of west

d. 62.2 units 54˚ north of west

V11. Arvin the Ant is on a picnic table. He travels 30 cm eastward, then 25 cm northward and finally 15 cm westward. What is the magnitude of Arvin’s net displacement?

a. 70 cm

b. 57 cm

c. 52 cm

d. 29 cm

V12. Arvin the Ant travels 30 cm eastward, then 25 cm northward and finally 15 cm westward. What is Arvin’s directional displacement with respect to his original position?

a. 59˚ N of E

b. 29˚ N of E

c. 29˚ N of W

d. 77˚ N of E

V13. A student adds two vectors with magnitudes of 200 and 40. Which one of the following is the only possible choice for the magnitude of the resultant?

a. 100

b. 200

c. 260

d. 40

V14. A string attached to a airborne kite is maintained at an angle of 40˚ with the horizontal. If a total of 120 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process (assume the kite string doesn’t sag)?

a. 100 m

b. 84 m

c. 77 m

d. 92 m

V15. Jack pulls a sled across a level field by exerting a force of 110 N at an angle of 30˚ with the ground. What are the parallel and perpendicular components, respectively, of this force with respect to the ground?

a. 64 N. 190 N

b. 190 N. 64 N

c. 95 N. 55 N

d. 55 N. 95 N

V16. A jogger runs halfway around a circular path with a radius of 60 m. What, respectively, are the displacement and distance jogged?

a. 60 m, 188 m

b. 120 m, 188 m

c. 0 m, 377 m

d. 120 m, 377 m

V17. Vector A is 3 units in length and points along the positive ´‑axis; vector B is 4 units in length and points along a direction 150˚ from the positive ´‑axis. What is the magnitude of the resultant when vectors A and B are added?

a. 7.0

b. 6.7

c. 4.7

d. 2.1

V18.     Vector A is 3 units in length and points along the positive ´‑axis; vector B is 4 units in length and points along a direction 150˚ from the positive ´‑axis. What is the direction of the resultant with respect to the positive ´‑axis?

            a. 77˚

            b. 13˚

            c. 86˚

            d. 103˚

19.  I walk six miles in a straight line in a direction north of east and I end up 2 miles east and several miles north. How many degrees north of east have I walked?

a. 19˚

b. 45˚

c. 60˚

d. 71˚

V20. Vector A points north and vector B points east. If C = B – A, then vector C points:

a. north of east

b. south of east

c. north of west

d. south of west

V21.     The first displacement is 6 m and the second displacement is 3 m. They cannot add together to give a total displacement of:

a. 2 m

b. 3 m

c. 6 m

d. 9 m

V22.     Five boys are pushing on a snowball, and each is pushing with a force of 10.0 N. However, each boy is pushing in a different direction. They are pushing north, northeast, east, southeast, and south. (Each boy is pushing at an angle of 45˚ relative to his neighbor.) What is the total push on the ball?

a. 0

b. 17.1 N

c. 24.1 N

d. 27.1 N

Chapter 1 & 2 – Answers               (vectors) - Answers