Question

As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. An equation to model the motion is y=20cos($\frac{\pi }{4}(t-3))+23$. Predict your height above the ground at a time of 1 seconds.

• A. $20.86ft$
• B. $23ft$
• C. $8.14ft$
• D. $18.96$

Answer 1

The correct option is B $23ft$

$y=20cos\left(\frac{\pi }{4}\right(t-3\left)\right)+23$

At $t=1$ second

Height above the ground,

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

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

$⟹y=23ft$. [ Since , $cos\left(\frac{-\pi }{4}\right)=0$ ]