Q: One light-year is equivalent to $$9.46 \times 10$$^{12}$$ meters. How many millimeters is this? Express your answer in scientific notation.

$$9.46 \times 10$$^{15}$$ \text{ mm}$

Q: If 1 light-year equals $$5.88 \times 10$$^{12}$$ miles, what is the distance in miles for 2.5 light-years?

$$1.47 \times 10$$^{13}$$ miles

Question 1

Which of the following correctly expresses 1 year in seconds using scientific notation?

Accepted Answer

$$3.15 	imes 10^7$ seconds

Question 2

One light-year is equivalent to $$9.46 	imes 10$$^{12}$$ meters. How many millimeters is this? Express your answer in scientific notation.

Accepted Answer

$$9.46 	imes 10$$^{15}$$ 	ext{ mm}$

Question 3

If 1 light-year equals $$5.88 	imes 10$$^{12}$$ miles, what is the distance in miles for 2.5 light-years?

Accepted Answer

$$1.47 	imes 10$$^{13}$$ miles

Question 4

Suppose you stack 100 sheets of paper, each 0.1 mm thick. What is the total height of the stack in meters?

Accepted Answer

$$0.01$$ meters

Question 5

If you stack 10,000 sheets of paper, each 0.1 mm thick, what is the most appropriate unit to express the height of the stack?

Accepted Answer

meters

Question 6

A right triangle has a base $$x = 3$$ meters and height $$y = 4$$ meters. What is the length of the hypotenuse $$d$$?

Accepted Answer

$$5$$ meters

Question 7

Given a right triangle with base $$x$$ and height $$y$$, which equation correctly gives the hypotenuse $$d$$?

Accepted Answer

$$d = \sqrt{x^2$ + y^2$}$$

Question 8

If a board is leaning against a wall making an angle $$	heta$$ with the ground, and the base is 2 meters from the wall while the height is 1 meter, what is $$	an(	heta)$$?

Accepted Answer

$$0.5$$

Question 9

You measure the angle $$	heta of a $$leaning object and find $$\sin(	heta) = 0.6. $$What is $$	heta in $$degrees?

Accepted Answer

$$36.9^\circ$$

Question 10

Given a right triangle with base $$x = 5$$ meters and hypotenuse $$d = 13$$ meters, what is $$\cos(	heta)$$?

Accepted Answer

$$0.385$$

Question 11

A vector $$\vec{A} = 3	ext{ inches} \hat{i} + 4	ext{ inches} \hat{j}. $$What is the magnitude $$|\vec{A}|$$?

Accepted Answer

$$5$$ inches

Question 12

If $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = 4\hat{i} + 1\hat{j}$$, what is $$\vec{C} = \vec{A} + \vec{B} in $$component form?

Accepted Answer

$$6\hat{i} + 4\hat{j}$$

Question 13

Given $$C_x = 6$$ and $$C_y = 8$$, what is the magnitude $$|\vec{C}|$$?

Accepted Answer

$$10$$

Question 14

If $$C_x = 6$$ and $$C_y = 8$$, and you calculate $$|\vec{C}| = 10$$, but your measured value is $$9.5$$, what is the percent difference?

Accepted Answer

$$5\%$$

Question 15

A stick of length $$L_o = 1.2$$ meters casts a shadow of length $$L_{sh} = 0.8$$ meters. What is the angle $$	heta$$ between the stick and the ground? (Use $$	an(	heta) = \frac{L_o}{L_{sh}})$$

Accepted Answer

$$56.3^\circ$$

Question 16

If your shadow is 1.5 meters long and your height is 1.8 meters, what is the tangent of the angle of elevation of the Sun?

Accepted Answer

$$1.2$$

Question 17

You measure your height using the shadow method and calculate $$h = 1.7$$ meters, but your actual height is $$1.75$$ meters. What is the percent error?

Accepted Answer

$$2.86\%$$

Question 18

If $$\sin(	heta) = 0.5$$, what is $$	heta in $$degrees?

Accepted Answer

$$30^\circ$$

Question 19

A vector $$\vec{B}$$ has a magnitude of 10 inches and points at $$60^\circ$$ above the horizontal. What is the $$y-$$component of $$\vec{B}$$?

Accepted Answer

$$8.66$$ inches

Physics Lab Study Guide: Measurement, Units, Trigonometry, and Vectors

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