1. The problem statement, all variables and given/known data
A ball with an initial speed of v1 = 21.5 m/s collides elastically with two identical balls whose centers are on a line perpendicular to the initial velocity and that are initially in contact with each other. The first ball is aimed directly at the contact point and all motion is frictionless.
>What is the speed of ball 1 after the collision?
>What is the speed of ball 2 after the collision?
2. Relevant equations
m1v1i + m2v2i = m1v1fcos(θ) + m2v2fcos(θ)
KE = 1/2 mv12 + 1/2 mv22
3. The attempt at a solution
So I know that the velocities have two components, x and y. I also know that at the collision point, the angle of the centers of mass are 30° (since the balls form an equilateral triangle).
For the x-component, I tried using the conservation of momentum equation above with cos(30°) and using the KE equation to substitute for unknown values of v1 and v2.
For the y-component I tried doing the same, but since the original velocity in the y-component is 0, I used
0 = m1v1sin(θ) + m2v2sin(30). For θ I tried 30, 60, and 180, but none of them worked.
Now I'm a bit stuck and I'm getting confused from all the variables I'm trying here. Any direction is appreciated!
A ball with an initial speed of v1 = 21.5 m/s collides elastically with two identical balls whose centers are on a line perpendicular to the initial velocity and that are initially in contact with each other. The first ball is aimed directly at the contact point and all motion is frictionless.
>What is the speed of ball 1 after the collision?
>What is the speed of ball 2 after the collision?
2. Relevant equations
m1v1i + m2v2i = m1v1fcos(θ) + m2v2fcos(θ)
KE = 1/2 mv12 + 1/2 mv22
3. The attempt at a solution
So I know that the velocities have two components, x and y. I also know that at the collision point, the angle of the centers of mass are 30° (since the balls form an equilateral triangle).
For the x-component, I tried using the conservation of momentum equation above with cos(30°) and using the KE equation to substitute for unknown values of v1 and v2.
For the y-component I tried doing the same, but since the original velocity in the y-component is 0, I used
0 = m1v1sin(θ) + m2v2sin(30). For θ I tried 30, 60, and 180, but none of them worked.
Now I'm a bit stuck and I'm getting confused from all the variables I'm trying here. Any direction is appreciated!
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