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

Answer:

Person will be 24 metres above the ground after 1.50 minutes

Step-by-step explanation:

Given:

$h(t)=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )$

To find:

time when the person be 24 meters above the ground

Solution:

Put $h(t)=24$

$h(t)=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )\\24=18.8-16.7\cos \left ( \frac{2\pi t}{5} \right )\\16.7\cos \left ( \frac{2\pi t}{5} \right )=18.8-24\\16.7\cos \left ( \frac{2\pi t}{5} \right )=-5.2\\\cos \left ( \frac{2\pi t}{5} \right )=\frac{-5.2}{16.7}\\\cos \left ( \frac{2\pi t}{5} \right )=-0.3114\\\frac{2\pi t}{5}=1.887\\\frac{2}{5}\times \frac{22}{7}t=1.887\\t=1.887\times \frac{5}{2}\times \frac{7}{22}\\=1.501\\\approx 1.50 \,\,minute$

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