Find v for the tip of the hour hand of a olook, if the hand is 7 om long.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Please help with the following homework question in the image.
![**Solve the problem.**
Find \( v \) for the tip of the hour hand of a clock, if the hand is 7 cm long.
**Explanation:**
To find the velocity (\( v \)) of the tip of the hour hand, you can use the formula for the linear velocity of a point on a rotating object. If the hour hand of a clock is considered to complete one full revolution (360 degrees) in 12 hours, you can calculate the velocity using the circumference of the path it travels.
First, calculate the circumference (\( C \)) of the circle described by the tip of the hour hand:
\[ C = 2\pi \times \text{radius} \]
Since the length of the hour hand is 7 cm, the radius of the circle is 7 cm. Thus,
\[ C = 2 \pi \times 7 = 14\pi \text{ cm} \]
The hour hand makes one full rotation in 12 hours. To find the linear velocity (\( v \)), divide the total distance traveled (circumference) by the time it takes to complete one revolution:
\[ v = \frac{C}{\text{Time}} = \frac{14\pi}{12} \text{ cm per hour} \]
\[ v = \frac{14\pi}{12} = \frac{7\pi}{6} \text{ cm per hour} \]
This calculation gives the linear velocity of the tip of the hour hand in centimeters per hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4283f212-ef6a-42bb-9a98-bd2f9ea72575%2F5945c392-d45d-4181-b31f-202a4523ce0b%2F8u4t1ar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve the problem.**
Find \( v \) for the tip of the hour hand of a clock, if the hand is 7 cm long.
**Explanation:**
To find the velocity (\( v \)) of the tip of the hour hand, you can use the formula for the linear velocity of a point on a rotating object. If the hour hand of a clock is considered to complete one full revolution (360 degrees) in 12 hours, you can calculate the velocity using the circumference of the path it travels.
First, calculate the circumference (\( C \)) of the circle described by the tip of the hour hand:
\[ C = 2\pi \times \text{radius} \]
Since the length of the hour hand is 7 cm, the radius of the circle is 7 cm. Thus,
\[ C = 2 \pi \times 7 = 14\pi \text{ cm} \]
The hour hand makes one full rotation in 12 hours. To find the linear velocity (\( v \)), divide the total distance traveled (circumference) by the time it takes to complete one revolution:
\[ v = \frac{C}{\text{Time}} = \frac{14\pi}{12} \text{ cm per hour} \]
\[ v = \frac{14\pi}{12} = \frac{7\pi}{6} \text{ cm per hour} \]
This calculation gives the linear velocity of the tip of the hour hand in centimeters per hour.
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