Distance Vs Another Problem

[perfectlovehe]

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:

 

[JaredJames]

Please use the correct formatting and show your attempt at this question as per PF guidelines.

Jared

 

[realcomfy]

You know the speed that the boys are moving (and thus the initial velocity of the bears) as well as their relative positions (which will give you the initial velocity vectors). You should be able to use the kinematic equations to solve for the trajectories of the bears once released and thus find how far apart they land.

What are the velocities of each of the boys and the moment they drop the bears?
What equations can you use to find the distance traveled?

 

[JaredJames]

Still going to need that attempt before I can help you.

Jared

 

[rwisz]

I would first start by breaking down the problem and identifying the key variables involved. The main variables in this scenario are the diameter of the Ferris wheel, the height of the bottom of the wheel, the speed at which the wheel is moving, and the positions of the boys on the wheel.

Next, I would use the given information to calculate the time it takes for the wheel to make one full rotation. Since the wheel has a diameter of 14.0 m and a speed of 1.0 m/s, it would take approximately 44 seconds for the wheel to make one full rotation (time = distance/speed).

Using this information, I can then calculate the distance traveled by the wheel in 44 seconds. This distance would be equal to the circumference of the wheel (2πr) which is approximately 44.0 m.

Now, we can focus on the positions of the boys and their teddy bears. Since they are seated at positions 45° from each other, we can use basic trigonometry to calculate the distance between the boys and their teddy bears. The distance between bear 1 and bear 2 would be equal to half the circumference of the wheel (22.0 m) multiplied by the sine of 45°, which is approximately 15.56 m. Similarly, the distance between bear 2 and bear 3 would also be 15.56 m.

Therefore, the final answer would be that the three teddy bears will land approximately 15.56 m apart from each other. This calculation assumes that the boys drop their bears at the exact same time and that there is no air resistance affecting the distance traveled by the bears.