A.) A Ferris wheel has a radius of 32 feet and completes one revolution every 5.4 minutes. What is the speed of the Ferris wheel (in radians per minute)?
_______radians per minute
B.) A Ferris wheel has a radius of 39 feet and travels 5.6 feet every second. What is the speed of the Ferris wheel (in radians per second)?
___________radians per second
C.) A Ferris wheel has a radius of 31 feet and travels 0.9 radians every 3 seconds. What is the speed of the Ferris wheel (in radians per second)?
_________radians per second
A. 1rev/5.4min * 6.28rad/rev = 1.16 rad/min.
B. Circumference = pi*2r = 3.14 * 78 = 245.0 feet.
5.6ft/s * 6.28rad/245ft. = 0.144 rad/s.
C. 0.9rad/3s = 0.3rad/s.
A.) To find the speed of the Ferris wheel in radians per minute, we need to convert the time taken for one revolution to minutes.
Given:
Radius of the Ferris wheel (r) = 32 feet
Time taken for one revolution (t) = 5.4 minutes
The circumference of the Ferris wheel is given by the formula C = 2πr.
C = 2π(32) = 64π feet
The speed of the Ferris wheel in radians per minute is given by the formula S = 2π/T, where T is the time taken for one revolution in minutes.
S = 2π/5.4 = (2π/5.4) * (1/1) = (2π/5.4) * (1/1) minutes^-1
Therefore, the speed of the Ferris wheel is (2π/5.4) radians per minute.
Answer: (2π/5.4) radians per minute.
B.) To find the speed of the Ferris wheel in radians per second, we need to convert the distance traveled per second to radians per second.
Given:
Radius of the Ferris wheel (r) = 39 feet
Distance traveled per second (d) = 5.6 feet
The circumference of the Ferris wheel is given by the formula C = 2πr.
C = 2π(39) = 78π feet
The speed of the Ferris wheel in radians per second is given by the formula S = d/C, where d is the distance traveled per second and C is the circumference of the Ferris wheel in feet.
S = (5.6/78π) * (2π/1) = (5.6/78) * (2/1) radians^-1
Therefore, the speed of the Ferris wheel is (5.6/78) radians per second.
Answer: (5.6/78) radians per second.
C.) To find the speed of the Ferris wheel in radians per second, we need to convert the time taken for a certain amount of radians to seconds.
Given:
Radius of the Ferris wheel (r) = 31 feet
Angle traveled (θ) = 0.9 radians
Time taken (t) = 3 seconds
The circumference of the Ferris wheel is given by the formula C = 2πr.
C = 2π(31) = 62π feet
The speed of the Ferris wheel in radians per second is given by the formula S = θ/t, where θ is the angle traveled in radians and t is the time taken in seconds.
S = (0.9/3) * (1/1) radians^-1
Therefore, the speed of the Ferris wheel is (0.9/3) radians per second.
Answer: (0.9/3) radians per second.
To find the speed of the Ferris wheel in radians per minute or radians per second, we need to use the formula:
Speed (in radians) = Distance traveled / Time taken
In the given problems, we are given the radius of the Ferris wheel, and the time or distance traveled. We can use this information to calculate the speed.
Let's solve each problem one by one:
A.) A Ferris wheel has a radius of 32 feet and completes one revolution every 5.4 minutes. To find the speed in radians per minute, we need to find the distance traveled in radians and divide it by the time taken.
The distance traveled in radians in one revolution is equal to the circumference of the circle (2πr) divided by 360 degrees. Since there are 2π radians in a circle, we can calculate the distance traveled in radians using the formula:
Distance (in radians) = (2πr) / 360
Substituting the given values, we get:
Distance (in radians) = (2π * 32) / 360
Now we can calculate the speed in radians per minute using the formula:
Speed (in radians per minute) = Distance (in radians) / Time taken
Plugging in the values, we get:
Speed (in radians per minute) = [(2π * 32) / 360] / 5.4
Simplifying this expression will give us the answer to part A.
B.) A Ferris wheel has a radius of 39 feet and travels 5.6 feet every second. To find the speed in radians per second, we need to find the distance traveled in radians and divide it by the time taken.
First, let's find the distance traveled in radians. We know that the distance traveled in radians is equal to the arc length divided by the radius. Using the formula:
Distance (in radians) = Arc length / Radius
Substituting the given values, we get:
Distance (in radians) = 5.6 / 39
Now we can calculate the speed in radians per second using the formula:
Speed (in radians per second) = Distance (in radians) / Time taken
Plugging in the values, we get:
Speed (in radians per second) = (5.6 / 39) / 1
Simplifying this expression will give us the answer to part B.
C.) A Ferris wheel has a radius of 31 feet and travels 0.9 radians every 3 seconds. To find the speed in radians per second, we can directly use the given values.
The speed in radians per second is equal to the distance traveled in radians divided by the time taken. Using the given values, we get:
Speed (in radians per second) = 0.9 / 3
Simplifying this expression will give us the answer to part C.