# Motion in Two Dimensions Question

1. Dec 15, 2013

### tacutamon

1. The problem statement, all variables and given/known data
Two thin rods are fastened to the inside of a circular ring as shown in the figure below. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods.

If the two beads are released from rest simultaneously from the positions shown, use your intuition and guess which bead reaches the bottom first.

2. Relevant equations
Equations for Red Ball:
(1) D = .5*g*t$^{2}$

Equations for Blue Ball:
(2) a$_{b}$ = g*sin(θ)

(3) L = .5*a$_{b}$*t$^{2}$

(4) L = D*sin(θ)

3. The attempt at a solution
The correct answer is that they will hit the ground at the same time. I am still curious in how I would explain this mathematically, rather than intuitively as the question states. I believe I have all the necessary equations to do so, but I am not sure how to compare them to show this. Would I show that subbing in equation 4 and 2 into equation 3 would give me equation 1?

Thanks so much for your help!

2. Dec 15, 2013

### TSny

Hello, tacutamon and welcome to PF!

Yes, that would work. Or, you could solve (1) for the red ball's time and solve (3) for the blue ball's time and try to show the times are equal.

3. Dec 15, 2013

### tacutamon

Thanks so much! That really clears up a lot.