To solve this problem we will apply the concepts related to the kinematic equations of linear motion. From there we will define the distance as the circumference of the earth (approximate as a sphere). With the speed given in the statement we will simply clear the equations below and find the time.
The circumference of the earth would be
Velocity is defined as,
Here , then
Therefore will take 167463.97 s or 1 day 22 hours 31 minutes and 3.97seconds
Answer:
(a) 0.261 rad/s
(b) 1007.72 m
Explanation:
The angular velocity of the Ferris wheel is 150.0 revolutions per hour.
(a) To calculate the angular velocity of the wheel in units of radians per second, you take into account the following equivalence:
1 hour = 3600 seconds
1 revolution = 2π radians
You use the previous conversion factors:
In units of radians per seconds the wheel turns at 0.261 rad/s
(b) To find the arc length described by the wheel, you first calculate the angle described by the wheel in the time t, by using the following formula:
(1)
ω: angular velocity = 0.261 rad/s
t: time = 4.95 min
You first convert the time to units of seconds
Next, you replace the values of the parameters in the equation (1):
Next, you use the following formula for the arc length:
(2)
r: radius of the wheel = 13.0 m
You replace the values of the parameters in the equation (2):
The arc length described by the wheel is 1007.72m