Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley $74.53 ^ { \circ }$ raises the pulley $16.0 \mathrm {~mm}$.
A) $12.10 \mathrm {~mm}$
B) $12.30 \mathrm {~mm}$
C) $12.40 \mathrm {~mm}$
D) $12.20 \mathrm {~mm}$

Question

Quizplus · Accepted Answer

To find the radius of the pulley, we can use the relationship between the angle of rotation in radians, the radius of the pulley, and the arc length (which is the distance raised). The formula is $ \theta = \frac{s}{r} $, where $ \theta $ is the angle in radians, $ s $ is the arc length (distance raised), and $ r $ is the radius of the pulley.First, convert the angle from degrees to radians: $ 74.53^\circ = 74.53 \times \frac{\pi}{180} $ radians.Then, rearrange the formula to solve for $ r $: $ r = \frac{s}{\theta} $.Substitute $ s = 16.0 $ mm (the distance raised) and $ \theta = 74.53 \times \frac{\pi}{180} $ radians into the formula:$$ r = \frac{16.0}{74.53 \times \frac{\pi}{180}} $$$$ r \approx 12.30 $$ mmTherefore, the radius of the pulley is approximately 12.30 mm, making choice B correct.

Assume That the Cities Lie on the Same North-South Line 74.53∘74.53 ^ { \circ }74.53∘

Assume That the Cities Lie on the Same North-South Line $74.53 ^ { \circ }$