Question

Tom is riding a Ferris wheel at a carnival. After a time t, his height H above the ground is given by the following formula.H=a cos(bt) + cFind Tom's height above the ground when a = -20 m, b = 3pi/5 rad/s, t=2 s, and c= 27 m.Do not round any intermediate computations. Round your answer to the nearest hundredth.

Answer 1

Given

The height(H) above the ground is represented by the formula below

$H\text{ = a cos(bt) + c}$$\begin{gathered} a\text{ = - 20m} \\ b\text{ = }\frac{30\pi}{5}\text{ rad/s} \\ t\text{ = 2s} \\ c\text{ = 27m} \end{gathered}$

Substituting the given values above, we can solve for the height.

Remember to evaluate the angle in Radians

$\begin{gathered} H\text{ = -20 cos(}\frac{3\pi}{5}\text{ }\times2)\text{ + 27} \\ =\text{ 43.18034} \\ \approx\text{ 43.18 m} \end{gathered}$

Hence, the height of Tom above the ground is 43.18 m