The Texas Star is a Ferris wheel at the state fair in Dallas. The Ferris wheel has a diameter of 61.8 m. To begin the ride, a passenger gets into a chair at the lowest point on the wheel, which is 2.7 m above the ground, as shown in the following diagram. A ride consists of multiple revolutions, and the Ferris wheel makes 1.5 revolutions per minute. Theheight of a chair above the ground, h, measured in metres, during a ride on the Ferris wheel can be modelled by the function h(t)=−a cos(bt)+d, where t is the time, in seconds, since a passenger began their ride.Calculate the value ofA ride on the Ferris wheel lasts for 12 minutes in total.For exactly one ride on the Ferris wheel, suggestBig Tex is a 16.7metre-tall cowboy statue that stands on the horizontal ground next to theFerris wheel. [Source: Aline Escobar., n.d. Cowboy. [image online] Available at: https://thenounproject.com/search/?q=cowboy&i=1080130This fileis licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en [Accessed 13/05/2021]. Source adapted.]There is a plan to relocate the Texas Star Ferris wheel onto a taller platform which will increasethe maximum height of the Ferris wheel to 65.2 m. This will change the value of one parameter,a, b or d, found in part (a).

The Texas Star is a Ferris wheel at the state fair in Dallas. The Ferris wheel has a diameter of $61.8 \text{m}$. To begin the ride, a passenger gets into a chair at the lowest point on the wheel, which is $2.7 \text{m}$ above the ground, as shown in the following diagram. A ride consists of multiple revolutions, and the Ferris wheel makes $1.5$ revolutions per minute.

Theheight of a chair above the ground, $h$, measured in metres, during a ride on the Ferris wheel can be modelled by the function $h\left(t\right)=-a \cos \left(bt\right)+d$, where $t$ is the time, in seconds, since a passenger began their ride.

Calculate the value of

A ride on the Ferris wheel lasts for $12$ minutes in total.

For exactly one ride on the Ferris wheel, suggest

Big Tex is a $16.7$metre-tall cowboy statue that stands on the horizontal ground next to theFerris wheel.

^{[Source: Aline Escobar., n.d. Cowboy. [image online] Available at: https://thenounproject.com/search/?q=cowboy&i=1080130
This fileis licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
https://creativecommons.org/licenses/by-sa/3.0/deed.en [Accessed 13/05/2021]. Source adapted.]}

There is a plan to relocate the Texas Star Ferris wheel onto a taller platform which will increasethe maximum height of the Ferris wheel to $65.2 \text{m}$. This will change the value of one parameter,$a$, $b$ or $d$, found in part (a).