1. ## Radian word problems- Ugrent

The revoling restauraunt in the CN Tower completes 5/6 of a revolution every hour. If two people ate dinner from 19:15 to 21:35, through what angle did there table rotate during the meal. Express your anwser in radian measure in exact form and in appoximate form, to the nearest tenth.

Also
A ferris wheel with a radius of 32m makes 2 revolutions every minute.
a) find the anglular volocity, in radians per second
b) if the ride last 3 min, how far does the ride travel, to the nearest meter?

Thanks so much

2. Originally Posted by musicismylife2007
1) The revoling restauraunt in the CN Tower completes 5/6 of a revolution every hour. If two people ate dinner from 19:15 to 21:35, through what angle did there table rotate during the meal. Express your anwser in radian measure in exact form and in appoximate form, to the nearest tenth.

2) Also
A ferris wheel with a radius of 32m makes 2 revolutions every minute.
a) find the anglular volocity, in radians per second
b) if the ride last 3 min, how far does the ride travel, to the nearest meter?

Thanks so much
Hello,

to 1)

1. Time difference: $\displaystyle 21:35 - 19:15 = 2 h \ 20 min = \frac73\ h$

2. Calculate the number of revolutions: $\displaystyle \frac73\ h \cdot \frac56\ \frac{rev}{h}=\frac{35}{18}\ rev$

3. Calculate the angle: $\displaystyle \left \{\begin{array}{l}1\ rev\ \longmapsto\ 2\pi\\ \frac{35}{18}\ rev \ \longmapsto\ \boxed{\frac{35 \pi}{9} \approx 12.2} \end{array}\right.$

to 2)
a) 2 revolutions in 1 minutes correspond with $\displaystyle 4\pi$ in 60 seconds. Thus the angular velocity is:

$\displaystyle \omega = \frac{4 \pi}{60\ s}=\frac{\pi}{15}\ s^{-1}$

b)In 3 minutes the wheel has done 6 revolutions. The distance covered by 1 revolution is: $\displaystyle p=2 \pi\ \cdot 32\ m=64 \pi \ \frac{m}{rev}$. Thus the total length of the ride is:

$\displaystyle r = 6\ rev \cdot 64 \pi \ \frac{m}{rev}=384 \pi\ m \approx 1206\ m$