Question

As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. An equation to model the motion is $y = 20\cos \left( {\dfrac{\pi }{4}(t - 3)} \right) + 23$. Predict your height above the ground at a time of 1 seconds.
A . 20.86ft
B . 23ft
C . 8.14ft
D . 18.96ft

Answer 1

Hint – In this problem we just have to put the value of t and get the answer to this problem using the value of cos 90.

Complete step-by-step answer:

The given equation is $y = 20\cos \left( {\dfrac{\pi }{4}(t - 3)} \right) + 23$

We need to find the height above the ground at t = 1 second.

So, on putting the value of t = 1 in the given equation we get,

$

  y = 20\cos \left( {\dfrac{\pi }{4}(1 - 3)} \right) + 23 \\

  y = 20\cos \left( {\dfrac{\pi }{4}( - 2)} \right) + 23 \\

  y = 20\cos \left( {\dfrac{{ - \pi }}{2}} \right) + 23 \\

  y = 23ft \\

$

Since, $\cos \dfrac{\pi }{2} = 0$.

Hence the answer is 23ft.

So, the correct option is B.

Note – To solve such problems we suggest you not to focus on the strange names of the appliances given but you need to focus only on the main part from which the answer can be calculated easily. Here we have given the equation of height varying sinusoidally in which time is a variable. We have been asked to find the height at time t = 1 second so we just put the value t = 1 in the equation and get the corresponding height.