The diameter of a ferris wheel is 250 feet and θ is the central angle formed as Dave travels around the wheel. Dave starts his ride at Point 0, makes 4 complete revolutions and stops at Point 1, 45 degrees from Point 0. If his ride takes 5 minutes, how fast was he going in miles per hour?
speed= radius*distance/time
= radius*(2PI*4+PI/4)/(1/12)
that gives it to you in feet/hour.
no change it to mph by dividing by 5280
A Ferris wheel has a radius of 50 feet. A person takes a seat and then the wheel turns 2pie/3. If it took 30 seconds for the wheel to turn 2pie/3, find (a). The distance the person traveled, (b). How fast the person was traveling, (c). The angular speed of the wheel.
C=3.14 * 250ft 785.4ft.=Circumference.
Revs = 4 + (360-45) / 360,
Revs = 4 + 315/360 = 4 7/8 = 4.875.
V=4.875rev/5min * 60min/hr=58.5rev/hr,
V=58.5rev/hr*785.4ft/rev*(1/5280)mi/ft
= 8.7mi/hr.
CORRECTION:
Revs = 4 + 45/360 = 4 1/8 = 4.125.
V=4.125rev/5min * 60min/hr = 49.5rev/hr
V=49.5rev/hr*785.4ft/rev*(1/5280)mi/ft
= 7.36mi/hr.
To find Dave's speed in miles per hour, we need to determine the distance he traveled in feet and then convert it to miles, taking into account his ride duration.
First, let's determine the distance Dave traveled on the ferris wheel in feet. Since the diameter of the ferris wheel is given as 250 feet, we can calculate the circumference using the formula:
Circumference = π * diameter
Substituting the given diameter:
Circumference = π * 250 feet
Next, let's find out how much of the circumference Dave traveled during his ride. We know that he made 4 complete revolutions and stopped at a position 45 degrees from his starting point. Since a complete circle is 360 degrees, the central angle he traveled can be calculated as follows:
θ = (number of revolutions * 360 degrees) + angle from the starting point
θ = (4 * 360 degrees) + 45 degrees
Now we can find the distance Dave traveled in feet by taking the fraction of the total circumference represented by the central angle:
Distance traveled = (θ / 360 degrees) * Circumference
Distance traveled = ( (4 * 360 degrees) + 45 degrees / 360 degrees) * (π * 250 feet)
Now, we can calculate Dave's speed in feet per minute:
Speed = Distance traveled / Ride duration
Speed = Distance traveled / 5 minutes
To convert the speed from feet per minute to miles per hour, we need to consider that 1 mile is equal to 5,280 feet, and 1 hour is equal to 60 minutes.
Speed (in miles per hour) = (Speed * 60 minutes) / (5,280 feet)
By applying these calculations, we will find Dave's speed in miles per hour.