At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50 meters and a diameter of 35 meters. It takes the wheel 5 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 50 meters? Round the answer to the nearest second.
The period:
2π/k = 5
then k = 2π/5
the amplitude = 35/2 = 17.5
your ferris wheel behaves like
h = 17.5sin(2π/5)
but you said it is 50 m high and the max height of the function is 17.5
so we need h = 17.5sin(2π/5) + 32.5
looks like I am overthinking this question.
Since you want to be at a height of 50 m, that height is reached after 1/4 rotation
or (1/4)of 5 minutes which is 1.25 minutes or 75 seconds
To solve this problem, we need to figure out how long it takes for your seat to reach a height of 50 meters.
First, let's find the circumference of the Ferris wheel. The circumference of a circle is calculated using the formula: C = π * d, where C is the circumference and d is the diameter.
Given that the diameter of the Ferris wheel is 35 meters, we can calculate the circumference as follows:
C = π * 35 = 110 meters.
Next, we need to determine how many revolutions the Ferris wheel makes in 5 minutes. Since one revolution takes 5 minutes, we can calculate the number of revolutions per minute by dividing 1 by 5: 1/5 = 0.2 revolutions per minute.
Now, we can calculate the speed at which the Ferris wheel rotates. We can determine the distance covered in one minute by multiplying the circumference by the number of revolutions per minute.
Distance covered in one minute = 0.2 * 110 = 22 meters.
Since we want to find out how long it takes for your seat to reach a height of 50 meters, we can divide the height by the distance covered in one minute:
Time required = 50 meters / 22 meters per minute.
To convert this time to seconds, we need to multiply by 60 because there are 60 seconds in one minute:
Time required in seconds = (50 meters / 22 meters per minute) * 60.
Calculating this value, we get:
Time required in seconds ≈ 136.36 seconds.
Rounding this value to the nearest second, we find that it would take approximately 136 seconds for your seat to reach a height of 50 meters on the Ferris wheel.
To find out how long it will take for your seat to reach a height of 50 meters, we need to determine the time it takes for the seat to go from the midline to the top of the ferris wheel.
First, let's find the circumference of the ferris wheel. We can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.
C = π * 35 meters
C ≈ 109.96 meters
Since the ferris wheel takes 5 minutes to make one revolution, we need to find the time it takes for the seat to go from the midline to the top of the ferris wheel.
The seat travels half the circumference to reach the top, so the time it takes is half of 5 minutes, or 2.5 minutes.
To convert minutes to seconds, we multiply by 60:
2.5 minutes * 60 seconds/minute = 150 seconds
Therefore, it will take approximately 150 seconds for your seat to reach a height of 50 meters.