A trigonometry problem, help ? ? ?

Question

Ok so it says,

Calculate the angular velocity in radians per minute of a Ferris wheel 250 ft. in diameter that takes 45 sec. to rotate once. Express the answer in terms of pi. For an answer I got 50pi/9min and well, I'm not sure its right...
Then it says to calculate linear velocity for the same problem and express it to the nearest foot per min. For this one I got 1178 ft/1min , but I'm not sure it's right either. So you can see my problem here, can you please help me out here, are these answers correct ? ? ?
Well thanks in advance. =)

Well I was certainly way off......not good. =( but O'well. .

Answer 1

PROBLEM 1:

The ferris wheel makes 1 complete turn (2 pi radians) in 3/4 minute.

2 pi .... n pi
------ = ------
3/4 ...... 1

2 pi = 3/4 n pi
n = 2 * 4/3
n = 8/3

So the answer is 8/3 pi radians per minute. That's 1 1/3 revolutions per minute.

PROBLEM 2:

Now for this part we need to consider the diameter, and I assume they are talking about the linear velocity of a point on the outer edge.

The circumference is 250 pi. In one minute, the ferris wheel will go around 1 1/3 times. That would be:
250 * 4/3 * pi ≈ 1,047.19755

Rounding we get 1,047 ft. / minute

Answer 2

For the first half you don't need to worry about the 250ft part, that's for the second half. There's 2pi radians in a circle (aka one complete rotation) So it goes thru 2pi per 45 seconds. 45s is three-quarters of a minute, so you have 2pi/.75mins you just hafta adjust the fraction so it's 1min on the bottom.

Then for the linear, you can take the angular times the RADIUS. (half the given diameter.)

;)

Answer 3

45 seconds = 45/60 minute
one rotation = 2π radians
Angular velocity
= 2π / (45/60)
= 8π/3 radians/minute.

Linear velocity = angular velocity x radius
= 8π/3 x 125 ft / minute
= 1000 π/3 ft / minute
= 1047 ft / minute

Answer 4

angular velocity
= 2 pi rad / 45 sec
= 2 pi rad / (45 (1/60) min)
= (8/3) pi rad/min,

linear velocity
= 2 pi (250/2) ft / 45 sec
= 250 pi ft / (45 (1/60) min)
= (1,000/3) pi ft/min
~= 1,047 ft/min.

by fidel_castro_001, grade 2, lol!!

Answer 5

P = 45 sec/rev
w = 1 rev/ 45 sec x 2 pi rad /1 rev x 60 sec/ 1 mi
= 2.67 pi rad/min

Answer 6

a) ω = θ/t
π = (2πrad/45 sec)(60 sec/1min) = (8/3)π/min ANS

b) v = ωr = (8/3)π/min x 250ft/2 = 1047.2 ft/min ANS

Hope I help you.

teddy boy

Answer 7

2π radians<-----> 3/4 min
ω = 2π / (3/4) radians / min
ω = 8π / 3 radians / min
ω = 8.38 radians / min


v = ω r
v = ( 8π / 3 ) (125) ft / min
v = 1047 ft / min