At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 100 meters and a diameter of 50 meters. It takes the wheel seven minutes to make one revolution. If you start your ride at the midline and the ferris wheel rotates counter clockwise, how many seconds will it take for your seat to reach a height of 75 meters? Round the answer to the nearest second.
To find the number of seconds it will take for your seat to reach a height of 75 meters on the Ferris wheel, we need to determine how much time it takes for the wheel to rotate from the midline to a height of 75 meters.
First, we need to find the circumference of the Ferris wheel, which is the distance it travels in one revolution. The circumference can be calculated using the formula:
Circumference = π * Diameter
Given that the diameter of the Ferris wheel is 50 meters, we can plug this value into the formula:
Circumference = π * 50 = 157.08 meters (rounded to two decimal places)
Next, we need to find the fraction of the circumference that represents a height of 75 meters. This can be done by dividing the desired height by the circumference:
Fraction = 75 / 157.08 ≈ 0.4779 (rounded to four decimal places)
Since the Ferris wheel takes seven minutes to make one revolution, we can use this information to calculate the time it takes for your seat to reach a height of 75 meters. We know that one revolution is equivalent to 360 degrees, and since the Ferris wheel rotates counterclockwise, we want to find the time it takes for the wheel to rotate through a fraction of 360 degrees equal to the fraction of the circumference that represents a height of 75 meters.
Time = (Fraction * 360 degrees) / 360 degrees * 7 minutes
Simplifying the expression, we have:
Time = Fraction * 7 minutes
Plugging in the value of the fraction we calculated earlier:
Time = 0.4779 * 7 minutes
Converting the time to seconds, we know that one minute is equal to 60 seconds:
Time = 0.4779 * 7 minutes * 60 seconds/minute
Calculating this expression, we find:
Time ≈ 201.59 seconds (rounded to the nearest second)
Therefore, it will take approximately 202 seconds for your seat to reach a height of 75 meters on the Ferris wheel.
amplitude is 25
let's use a sine curve function
and let's start with
h = 25sin kt
we want the period to be 7
2π/k = 7
k = 2π/7
so h = 25 sin 2π/7 t
the max of that curve is 25 but we want it to be 100
so we have to raise our function by 75
h = 25 sin 2π/7 t + 75 , where t is in minutes
Not sure what you mean by "If you start your ride at the midline"
Since the max height is to be 100m and the diameter is 50 m, then your lowest point and your entry point is 50 m above the ground.
so the axis of the ferris wheel must be 75 m above the ground.
So according to my interpretation, I have the following critical points
t=0, h = 50
t = (1/4)7 , h = 75
t = (1/2)7 , h = 100
t = (3/4)(7) , h = 75
t = 7 , h = 50
time to reach 75 m is 7/4 minutes or 1.75 minutes
I think the last part is all we really had to do, and I overthought the question.
I still would have had to do a phase shift to match my equation so that when t = 0 , h = 50