Question

The table of values shows the height of a car of a Ferris wheel as it travels in a circular motion. Which statements are true? Select each correct answer.

The car makes a complete revolution in 12 s

The maximum height of the Ferris wheel above ground is 50 yd.

If the car is loaded at 0s, then people are loaded at the lowest height of the Ferris wheel.
The radius of the Ferris wheel is 25 yd​

Answer 1

The true statements are;

The car makes one complete revolution in 12 s

The radius of the Ferris wheel is 25 yd

Explanation:

The values of the table of the given Ferris wheel are presented here as follows;

`\begin{array}{cc}Time \ (seconds) &Height \ (yards)\\0&30\\3&55\\6&30\\9&5\\12&30\\15&55\\18&30\\21&5\\24&30\end{array}`

From the table, we have;

The time it takes the Ferris wheel to complete a motion round from a height of 30 yards and back to 30 yards which is one revolution = 12 s

∴ The time it takes the car to complete one revolution = 12 s

The maximum height of the Ferris wheel = 55 yards

The lowest height of the Ferris wheel = 5 yards

The time at which the Ferris wheel is at the lowest height = 9 s, and 21 s

If the car is loaded at 0 s, then people are loaded above the lowest height of the Ferris wheel

The diameter of the Ferris wheel = The maximum height of the Ferris wheel - The minimum height of the Ferris wheel

∴ The diameter of the Ferris wheel = 55 yards - 5 yards = 50 yards

The radius of the Ferris wheel, R = 1/2 × The diameter of the Ferris wheel

∴ The radius of the Ferris wheel, R = 1/2 × 50 yards = 25 yards

Therefore, the true statements are;

The car makes one complete revolution in 12 s

The radius of the Ferris wheel is 25 yd.