Question

Suppose that the height above ground of a person sitting on a Ferris wheel is described by the following.

h(t)=18.8-16.7cos((2pi/5)t)
In this equation, "h(t)" is the height above ground (in meters) and "t" is the time (in minutes). The ride begins at t=0 minutes.
During the first 5 minutes of the ride, when will the person be 24 meters above the ground?
Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute.

Answer 1

Person will be 24 metres above the ground after 1.50 minutes

Explanation:

Given:

`h(t)=18.8-16.7\cos \left ( (2\pi t)/(5) \right )`

To find:

time when the person be 24 meters above the ground

Solution:

Put
`h(t)=24`

`h(t)=18.8-16.7\cos \left ( (2\pi t)/(5) \right )\\24=18.8-16.7\cos \left ( (2\pi t)/(5) \right )\\16.7\cos \left ( (2\pi t)/(5) \right )=18.8-24\\16.7\cos \left ( (2\pi t)/(5) \right )=-5.2\\\cos \left ( (2\pi t)/(5) \right )=(-5.2)/(16.7)\\\cos \left ( (2\pi t)/(5) \right )=-0.3114\\(2\pi t)/(5)=1.887\\(2)/(5)* (22)/(7)t=1.887\\t=1.887* (5)/(2)* (7)/(22)\\=1.501\\\approx 1.50 \,\,minute`

So, the person will be 24 metres above the ground after 1.50 minutes