Q: The density of mercury is $$13.5~\text{g/cm}^3. $$What is this value in $$\text{kg/m}^3$$?

$$1.35 \times 10^4$~\text{kg/m}^3$$

Q: If the average car in the US is driven $$10,000~\text{mi}$$ per year and gets $$20~\text{mi/gal}$$, and there are two cars for every three people in a population of $$3.3 \times 10^8$, how many gallons of gasoline are used per day?

$$8.9 \times 10^7$~\text{gal/day}$$

Q: Given vector $$\vec{A}$$ has $$A_x = 0$$ and $$A_y = -8.00~\text{m}$$, what is the magnitude and direction of $$\vec{A}$$?

Magnitude: $$8.00~\text{m}$$, Direction: $$270^\circ$$ from $$+x$$ axis

Q: If $$\vec{A} = 8.00~\text{m} at$$ $$270^\circ$$, $$\vec{B} = 15.0~\text{m} at$$ $$30.0^\circ$$, $$\vec{C} = 12.0~\text{m} at$$ $$205^\circ$$, and $$\vec{D} = 10.0~\text{m} at$$ $$143^\circ$$, what is $$B_x$$ and $$B_y$$?

$$B_x = 7.50~\text{m},\ B_y = 13.0~\text{m}$$

Question 1

A car travels 1.70 miles. Using the conversion factors $$1~	ext{mi} = 5280~	ext{ft}$$, $$1~	ext{ft} = 12~	ext{in}$$, $$1~	ext{in} = 2.54~	ext{cm}$$, $$1~	ext{m} = 100~	ext{cm}$$, and $$1~	ext{km} = 1000~	ext{m}$$, how many kilometers did the car travel?

Accepted Answer

$$2.74~	ext{km}$$

Question 2

A bottle contains $$0.473~	ext{L} of $$salad dressing. Using $$1~	ext{L} = 1000~	ext{cm}^3$$ and $$1~	ext{in} = 2.54~	ext{cm}$$, what is the volume in cubic inches?

Accepted Answer

$$28.9~	ext{in}^3$$

Question 3

The density of mercury is $$13.5~	ext{g/cm}^3. $$What is this value in $$	ext{kg/m}^3$$?

Accepted Answer

$$1.35 	imes 10^4$~	ext{kg/m}^3$$

Question 4

A rectangular piece of sheet metal is measured to be $$14~	ext{mm}$$ long and $$6.98~	ext{mm}$$ wide. What is the area in $$	ext{mm}^2$$ with the correct number of significant figures?

Accepted Answer

$$98~	ext{mm}^2$$

Question 5

If the average car in the US is driven $$10,000~	ext{mi}$$ per year and gets $$20~	ext{mi/gal}$$, and there are two cars for every three people in a population of $$3.3 	imes 10^8$, how many gallons of gasoline are used per day?

Accepted Answer

$$8.9 	imes 10^7$~	ext{gal/day}$$

Question 6

A postal employee drives a route with three displacements: $$2.6~	ext{km}$$ east, $$4.0~	ext{km}$$ north, and $$3.1~	ext{km}$$ west. What is the magnitude of the resultant displacement?

Accepted Answer

$$7.8~	ext{km}$$

Question 7

Given vector $$\vec{A}$$ has $$A_x = 0$$ and $$A_y = -8.00~	ext{m}$$, what is the magnitude and direction of $$\vec{A}$$?

Accepted Answer

Magnitude: $$8.00~	ext{m}$$, Direction: $$270^\circ$$ from $$+x$$ axis

Question 8

A vector $$\vec{A}$$ has $$A_x = -16.2~	ext{m}$$ and makes an angle of $$42.0^\circ$$ counterclockwise from the $$+y$$ axis. What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$24.2~	ext{m}$$

Question 9

Given $$\vec{A} = -2.00\,\hat{i} + 3.00\,\hat{j} + 6.00\,\hat{k}$$ and $$\vec{B} = 3.00\,\hat{i} + 2.00\,\hat{j} - 3.00\,\hat{k}$$, what is $$|\vec{A} - \vec{B}|$$?

Accepted Answer

$$10.3$$

Question 10

The scalar product of $$\vec{A} = 3.80\,\hat{i} + 6.90\,\hat{j}$$ and $$\vec{B} = 5.20\,\hat{i} - 2.10\,\hat{j} is$$:

Accepted Answer

$$5.27$$

Question 11

If two vectors $$\vec{A}$$ and $$\vec{B}$$ have a scalar product of $$-9.00$$ and a vector product magnitude of $$4.00$$, what is the angle between them?

Accepted Answer

$$156^\circ$$

Question 12

A force $$\vec{F} of$$ $$7.00~	ext{N}$$ acts at $$60.0^\circ$$ above the $$-x$$ axis, and the displacement is $$0.800~	ext{m} in $$the $$+x$$ direction. What is the work done by $$\vec{F}$$?

Accepted Answer

$$-2.80~	ext{J}$$

Question 13

A hybrid car gets $$55.0~	ext{mi/gal}. $$Convert this to $$	ext{km/L}$$ using $$1~	ext{mi} = 1.609~	ext{km}$$ and $$1~	ext{gal} = 3.788~	ext{L}.$$

Accepted Answer

$$23.4~	ext{km/L}$$

Question 14

If $$\vec{A} = 8.00~	ext{m} at$$ $$270^\circ$$, $$\vec{B} = 15.0~	ext{m} at$$ $$30.0^\circ$$, $$\vec{C} = 12.0~	ext{m} at$$ $$205^\circ$$, and $$\vec{D} = 10.0~	ext{m} at$$ $$143^\circ$$, what is $$B_x$$ and $$B_y$$?

Accepted Answer

$$B_x = 7.50~	ext{m},\ B_y = 13.0~	ext{m}$$

Question 15

Given two forces $$F_1$$ and $$F_2$$ with constant magnitudes, and the resultant force is $$8.00~	ext{N}$$ when the angle between them is $$0^\circ$$, $$7.43~	ext{N} at$$ $$45^\circ$$, $$7.00~	ext{N} at$$ $$60^\circ$$, and $$5.83~	ext{N} at$$ $$90^\circ$$, what is the magnitude of the larger force?

Accepted Answer

$$5.00~	ext{N}$$

Question 16

How many nanoseconds does it take light to travel $$5.50~	ext{ft} in $$vacuum? ($$c = 3.00 	imes 10^8$~	ext{m/s}$$, $$1~	ext{ft} = 0.3048~	ext{m})$$

Accepted Answer

$$5.59~	ext{ns}$$

Question 17

If you are $$1.60$$ billion seconds older, how many years is that? (Assume $$1~	ext{year} = 365~	ext{days})$$

Accepted Answer

$$50.7~	ext{years}$$

Finding the Components of Vectors from a Diagram

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