Question

The London Eye is a giant Ferris wheel in London with a diameter of 120 m. The wheel passenger capsules are attached to the circumference of the wheel, and the wheel rotates at 26 cm per second. Solve to find.

a) The length that a passenger capsule would travel if the wheel makes a rotation of 2000.
b) The time, in minutes, that it would take for the passenger capsule to make a rotation of 2000.
c) The time, in minutes, that it would take for a passenger capsule to make a full revolution.

Answer 1

Answer:

Answer:

a

   x = 209.5 \ mx=209.5 m

b

  t = 13.4 \ minutest=13.4 minutes

c

  t_v = 24 \ minutestv=24 minutes

Step-by-step explanation:

From the question we are told that

   The diameter is  d  =  120 m

    The  speed of the wheels is v = 26 \ cm / s = 0.26 \ m/sv=26 cm/s=0.26 m/s

 Generally the radius is mathematically represented as

          r = \frac{d}{2} = \frac{120}{2} = 60 \ mr=2d=2120=60 m

 Generally the circumference is  mathematically evaluated as

        C= 2 \pi rC=2πr    

        C= 2 * 3.142 * 60C=2∗3.142∗60    

         C= 377.04 \ mC=377.04 m

Generally  

        C  \to \ 360^o→ 360o

        x    \to \ 200^o→ 200o

=>     x = \frac{C * 200}{360}x=360C∗200

=>     x = \frac{ 377.04* 200}{360}x=360377.04∗200        

=>     x = 209.5 \ mx=209.5 m

 Generally the angular speed is mathematically evaluated as

        w = \frac{v}{r}w=rv

=>     w = \frac{0.26}{60}w=600.26

=>     w = 0.00433 \ rad/sw=0.00433 rad/s

Generally

      1 \ radian \to 57.2958^o1 radian→57.2958o

      z  radian  \to 200^o→200o

=>    z = \frac{200}{57.2958}z=57.2958200

=>    z = 3.49 \ radianz=3.49 radian

Generally the time taken is mathematically evaluated as

       t = \frac{z}{w}t=wz

=>    t = \frac{3.49}{0.00433}t=0.004333.49

=>    t = 806.2 \ st=806.2 s

Converting to minutes

       t = \frac{806.2}{60}t=60806.2

       t = 13.4 \ minutest=13.4 minutes

Generally given that one resolution is equal to  360° so

      1 \ radian \to 57.2958^o1 radian→57.2958o

      v  radian  \to 360^o→360o

=>    v = \frac{360}{57.2958}v=57.2958360

=>    v = 6.28 \ radianv=6.28 radian

Generally the time taken is mathematically evaluated as

       t_v = \frac{v}{w}tv=wv

     =>    t_v = \frac{6.28}{0.00433}tv=0.004336.28

        =>    t_v = 1451.1 \ stv=1451.1 s

Converting to minutes

          =>    t_v = \frac{1451.1}{60}tv=601451.1  

          =>    t_v = 24 \ minutestv=24 minutes