Q: A cross-country skier travels 1.00 km north and then 2.00 km east. What is the direction of her resultant displacement from the starting point?

$$\phi = \tan$$^{-1}$$\left(\frac{2.00}{1.00}\right) = 63.4^\circ$$ east of north

Question 1

Which of the following statements best describes the difference between a scalar and a vector quantity?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 2

A car travels 60 km east and then 80 km north. What is the magnitude of its displacement from the starting point?

Accepted Answer

$$\sqrt{60^2$ + 80^2$} = 100 km$$

Question 3

When multiplying or dividing measured quantities, the number of significant figures in the result should be determined by:

Accepted Answer

The factor with the fewest significant figures.

Question 4

Given $$\vec{A}$$ and $$\vec{B}$$ are vectors, which of the following is true about vector addition?

Accepted Answer

$$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 5

A vector $$\vec{A}$$ has a magnitude of 5 units and makes an angle of $$53^\circ$$ with the x-axis. What are its x and y components?

Accepted Answer

$$A_x = 5 \cos 53^\circ = 3.0$$, $$A_y = 5 \sin 53^\circ = 4.0$$

Question 6

If $$\vec{A}$$ and $$\vec{B}$$ are antiparallel vectors with magnitudes $$A$$ and $$B$$, what is the magnitude of their sum $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$C = |A - B|$$

Question 7

A cross-country skier travels 1.00 km north and then 2.00 km east. What is the direction of her resultant displacement from the starting point?

Accepted Answer

$$\phi = 	an$$^{-1}$$\left(\frac{2.00}{1.00}ight) = 63.4^\circ$$ east of north

Question 8

Which of the following is the correct way to subtract vector $$\vec{B}$$ from vector $$\vec{A}$$?

Accepted Answer

$$\vec{A} - \vec{B} = \vec{A} + (-\vec{B})$$

Question 9

If a vector $$\vec{A} is $$multiplied by a negative scalar $$-3$$, what happens to the vector?

Accepted Answer

Its magnitude is tripled and its direction is reversed.

Question 10

A measurement is recorded as $$2.20 	imes 10^3$ m. How many significant figures does this value have?

Accepted Answer

Three

Question 11

A student adds $$27.153$$, $$138.2$$, and $$11.74. $$According to the rules for significant figures, what is the correct sum?

Accepted Answer

$$153.6$$

Question 12

The rest energy $$E of an $$electron is calculated using $$E = mc^2$. If m = 9.11$$ 	imes $$10^{-31} kg $$and $$c = 2.99792458 	imes 10^8$ m/s, what is E$ to three significant figures?

Accepted Answer

$$8.19 	imes 10$$^{-14}$$ J

Question 13

Which of the following best describes the commutative law for vector addition?

Accepted Answer

$$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 14

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is the magnitude of their sum $$\vec{C}$$?

Accepted Answer

$$C = \sqrt{A^2$ + B^2$}$$

Question 15

A plane is flying at $$100 km/h$$ $$30^\circ$$ north of east. The wind is blowing at $$20 km/h$$ $$45^\circ$$ south of west. Which method would you use to find the plane's ground speed and direction?

Accepted Answer

Add the velocity vectors graphically using the tip-to-tail method and resolve into components.

Question 16

Which of the following is the correct formula for the x-component of a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the x-axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 17

Which of the following is NOT a correct statement about vectors?

Accepted Answer

The sum of two vectors is always greater than the magnitude of either vector.

Units, Physical Quantities, and Vectors: Study Notes for College Physics I

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