IT'S TIMED URGENT
A person sitting on a Ferris wheel rises and falls as the wheel turns. Suppose that the person's height above ground is described by the following function.
h(t)= 21.7 + 19.2 cos 1.4t
In this equation, h(t) is the height above ground in meters, t is the time in minutes.
Find the following. If necessary, round to the nearest hundredth.
Period of h _ minutes
Number of revolutions per minute : __
Amplitude of h : __ meters
To find the period of the function h(t), we need to determine the time it takes for the function to repeat its pattern. In this case, the function represents the height of a person on a Ferris wheel, so it goes through a complete cycle when the person ends up at the same height above the ground.
The general formula for the period of a cosine function is T = 2π / b, where b is the coefficient of t in the function.
In the given equation h(t) = 21.7 + 19.2 cos(1.4t), the coefficient of t is 1.4.
So, T = 2π / 1.4 = 4π / 2.8 ≈ 4.487.
Therefore, the period of h is approximately 4.49 minutes.
To find the number of revolutions per minute, we need to determine how many complete cycles the person goes through in one minute. Since the period is 4.49 minutes, we can divide 1 minute by the period to find the number of cycles.
Number of revolutions per minute = 1 / 4.49 ≈ 0.22 (rounded to the nearest hundredth).
Therefore, the number of revolutions per minute is approximately 0.22.
To find the amplitude of h, we need to identify the maximum and minimum values of the function. In this case, the maximum value is the amplitude since the cosine function oscillates between -1 and 1.
The amplitude of a cosine function is equal to the absolute value of the coefficient in front of the cosine term. In the given equation h(t) = 21.7 + 19.2 cos(1.4t), the coefficient in front of cos(1.4t) is 19.2.
Therefore, the amplitude of h is 19.2 meters.