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Question 1 of 5: Solve each word problem:
Beth needs to cut the grass. To get the engine to turn over, the pulley must turn at 10,800 revolutions per hour. The pulley has radius of 2.4 inches. What is the needed angular speed of the pulley in radians per second? How fast does Beth need to pull the cord in order to start the lawnmower?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$ω=\frac{7 π \hspace{.2em}\text{radians}}{1 \hspace{.1em}\text{second}}$$ $$v=\frac{14.8 π \hspace{.2em}\text{feet}}{1 \hspace{.1em}\text{second}}$$
B
$$ω=\frac{19 π \hspace{.2em}\text{radians}}{1 \hspace{.1em}\text{second}}$$ $$v=\frac{12 π \hspace{.2em}\text{feet}}{1 \hspace{.1em}\text{second}}$$
C
$$ω=\frac{8 π \hspace{.2em}\text{radians}}{1 \hspace{.1em}\text{second}}$$ $$v=\frac{7 π \hspace{.2em}\text{feet}}{1 \hspace{.1em}\text{second}}$$
D
$$ω=\frac{6 π \hspace{.2em}\text{radians}}{1 \hspace{.1em}\text{second}}$$ $$v=\frac{1.2 π \hspace{.2em}\text{feet}}{1 \hspace{.1em}\text{second}}$$
E
$$ω=\frac{5 π \hspace{.2em}\text{radians}}{1 \hspace{.1em}\text{second}}$$ $$v=\frac{3.5 π \hspace{.2em}\text{feet}}{1 \hspace{.1em}\text{second}}$$
Question 2 of 5: Solve each word problem:
A windmill blade with a 30-inch diameter makes 7200 revolutions per hour. What is the linear speed in inches per second of the windmill blade?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$v=\frac{25 π \hspace{.15em}\text{inches}}{1 \hspace{.15em}\text{second}}$$
B
$$v=\frac{113.8 π \hspace{.15em}\text{inches}}{1 \hspace{.15em}\text{second}}$$
C
$$v=\frac{19.5 π \hspace{.15em}\text{inches}}{1 \hspace{.15em}\text{second}}$$
D
$$v=\frac{33 π \hspace{.15em}\text{inches}}{1 \hspace{.15em}\text{second}}$$
E
$$v=\frac{60 π \hspace{.15em}\text{inches}}{1 \hspace{.15em}\text{second}}$$
Question 3 of 5: Solve each word problem:
A toy drone has blades that rotate 5400 times per minute. If the length of each blade is 14 centimeters, what is the linear speed in centimeters per second?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$v=\frac{595 π \hspace{.15em}\text{cm}}{1 \hspace{.15em}\text{second}}$$
B
$$v=\frac{375 π \hspace{.15em}\text{cm}}{1 \hspace{.15em}\text{second}}$$
C
$$v=\frac{1260 π \hspace{.15em}\text{cm}}{1 \hspace{.15em}\text{second}}$$
D
$$v=\frac{945 π \hspace{.15em}\text{cm}}{1 \hspace{.15em}\text{second}}$$
E
$$v=\frac{480 π \hspace{.15em}\text{cm}}{1 \hspace{.15em}\text{second}}$$
Question 4 of 5: Solve each word problem:
A carousel at the school fair makes 180 revolutions per hour. Bob is riding a horse that is 270 inches from the center. What is Bob's linear speed in feet per second?
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$v = \frac{3.5π \hspace{.15em}\text{ft}}{1 \hspace{.15em}\text{second}}$$
B
$$v = \frac{2.25π \hspace{.15em}\text{ft}}{1 \hspace{.15em}\text{second}}$$
C
$$v = \frac{5.7π \hspace{.15em}\text{ft}}{1 \hspace{.15em}\text{second}}$$
D
$$v = \frac{6.9π \hspace{.15em}\text{ft}}{1 \hspace{.15em}\text{second}}$$
E
$$v = \frac{12.8π \hspace{.15em}\text{ft}}{1 \hspace{.15em}\text{second}}$$
Question 5 of 5: Solve each word problem:
At a local sewing factory, thread is being pulled off a spool at the rate of 2.1384 kilometers per hour. Find the radius of the spool in centimeters if it makes 152 revolutions per minute. Round your answer to the nearest hundredth.
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$r ≈ 3.73\hspace{.15em}\text{cm}$$
B
$$r ≈ 5.92\hspace{.15em}\text{cm}$$
C
$$r ≈ 8.11\hspace{.15em}\text{cm}$$
D
$$r ≈ 13\hspace{.15em}\text{cm}$$
E
$$r ≈ 2.92\hspace{.15em}\text{cm}$$

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