Question

A Ferris wheel at a carnival has a radius of 38 feet. Suppose a passenger is traveling at 5 miles per hour. (A usual fact: 1 mi = 5280 ft).A) Find the angular speed of the wheel in radians per minute.B) Find the number of revolutions the wheel makes per hour.

Answer 1

Answer:

a

$w =  11.58 \ rad/minutes$

b

$R_h  =  111 \ revolution\ per  \  hour$

Step-by-step explanation:

From  the question we told that

    The radius of the wheel is  $r = 38 \  ft$

     The  speed of the passenger is  $v  =  5 \  miles /hr = \frac{26400}{3600} = 7.33 \ ft / s$

  Generally the angular speed is mathematically represented as

     $w =  \frac{v}{r}$

=>   $w =  \frac{7.3}{ 38}$

=>   $w =  0.193 \ rad/s$

now converting the seconds to minutes

        $w =  0.193 *60$

        $w =  11.58 \ rad/minutes$

Generally number of revolutions the wheel makes per minutes is mathematically represented as

     $R = \frac{11.58 }{2 \pi}$

      $R = 1.84 \ rpm$

Generally number of revolutions the wheel makes per hour  is mathematically represented as

       $R_h  =   R *  60$

=>     $R_h  =  1.84 * 60$

=>    $R_h  =  111 \ revolution\ per  \  hour$