Find the linear speed in feet per minute of a seat on the Ferris wheel.

v= r.w

How do I find out "w"?

r= 25 ft.
arc= 40 ft.
angle= 58°
1 revolution= 157 ft./revolution

To find the angular speed, w, we need to use the given information.

First, we know that one revolution corresponds to an arc length of 157 ft. Therefore, we can calculate the angle subtended by this arc using the formula:

angle = (arc length / radius) * (180° / π)

Plugging in the given values:
angle = (40 ft / 25 ft) * (180° / π) ≈ 41.47°

So, we know that for one revolution, the angle subtended is approximately 41.47°.

Now, to find the angular speed, we need to relate it to the time taken to complete one revolution. Since we want the linear speed in feet per minute, we can use the formula:

v = r * w

where v is the linear speed, r is the radius, and w is the angular speed.

To find w, we need to convert the angle to radians:
angle (in radians) = angle * (π / 180°)
angle (in radians) = 41.47° * (π / 180°) ≈ 0.724 radians

Now, we can rearrange the formula to solve for w:
w = v / r

Given that r = 25 ft, we need to find v first.

To convert the linear speed in feet per minute, we can use the information that one revolution corresponds to an arc length of 157 ft:
v = 157 ft / 1 revolution

Since we want the speed in feet per minute, we need to convert revolutions to minutes. Let's assume that the Ferris wheel takes t minutes to complete one revolution.

v = 157 ft / t

Now that we have v, we can find w:

w = v / r
w = (157 ft / t) / 25 ft

Simplify the expression:
w = 157 / (25 * t) revolutions per minute

Therefore, to find the angular speed, w, you need to know the time taken to complete one revolution, t.