At a county fair, a boy and two friends bring their teddy bears on the giant Ferris wheel. The wheel has a diameter of 14.0 m, the bottom of the wheel is 1.9 m above the ground and its rim is moving at a speed of 1.0 m/s. The boys are seated in positions 45° from each other. When the wheel brings the second boy to the maximum height, they all drop their stuffed animals. How far apart will the three teddy bears land? (Assume that the boy on his way down drops bear 1, and the boy on his way up drops bear 3.)

distance between bears 1 and 2
distance between bears 2 and 3

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To find the distances between the teddy bears, we first need to find the positions of the teddy bears on the Ferris wheel. Since there are three boys and they are seated 45° apart, we can divide the circle into 8 equal angles (360°/45°).

Let's assign the teddy bear positions as follows:
Bear 1: Boy 1
Bear 2: Boy 2
Bear 3: Boy 3

Now, let's calculate their positions:

Position of Bear 1 (Boy 1):
The boy is at the bottom of the Ferris wheel, so his position angle is 0°.

Position of Bear 2 (Boy 2):
Since the boys are seated 45° apart, Boy 2 is 45° clockwise from Boy 1.
Position angle of Boy 2 = 0° + 45° = 45°

Position of Bear 3 (Boy 3):
Similarly, Boy 3 is 45° clockwise from Boy 2.
Position angle of Boy 3 = 45° + 45° = 90°

Now, let's calculate the distances between the bears:

Distance between Bears 1 and 2:
To find this distance, we need to calculate the arc length between their positions on the Ferris wheel.
The arc length is given by: arc length = (angle in radians) x (radius of the wheel)

Radius of the wheel = diameter/2 = 14.0 m/2 = 7.0 m

Angle in radians = (position angle of Boy 2 - position angle of Boy 1) x (pi/180)

Angle in radians = (45° - 0°) x (pi/180) = 45° x (pi/180) = (45pi/180) = (pi/4)

Arc length between Bears 1 and 2 = (pi/4) x (7.0 m) = (7pi/4) ≈ 5.497 m

Therefore, the distance between Bears 1 and 2 is approximately 5.497 meters.

Distance between Bears 2 and 3:
To find this distance, we follow the same steps as above.
Angle in radians = (position angle of Boy 3 - position angle of Boy 2) x (pi/180)

Angle in radians = (90° - 45°) x (pi/180) = 45° x (pi/180) = (45pi/180) = (pi/4)

Arc length between Bears 2 and 3 = (pi/4) x (7.0 m) = (7pi/4) ≈ 5.497 m

Therefore, the distance between Bears 2 and 3 is also approximately 5.497 meters.