Question

Andres boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 4.7 radians per minute and has a radius of 30 feet. Let t represent the number of seconds since the Ferris wheel started rotating. a. Write an expression (in terms of t) to represent the varying number of radians 8 Ryan has swept out since the ride started. Preview s height (in feet) above Preview c. Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground.

Answer 1

Answer:

a) r(t) = 0.783t radians

b) h(t) = 30cos(0.783*t) feet

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply using the fact that 1 min = 60 seconds

4.7 radians __________ 60 seconds

r(t) radians ____________  t seconds

$\large \displaystyle\frac{4.7}{r(t)}=\displaystyle\frac{60}{t}\Rightarrow r(t)=(4.7/60)t \Rightarrow\\\\\boxed{r(t)=0.783t\;rad}$

The height h(t) after t seconds is given by

h(t) = 30cos(r(t)) ===>

h(t) = 30cos(0.783*t) feet