Two Balls Colliding. Check my work please

In summary, the conversation discussed the equations v=v0-gt and uy=u0sinx-gt, and how at the highest point, both balls have to be at their highest point. It was also mentioned that equating the two times, u0sinx=v0, which is obvious without calculation. It was then concluded that u0=v0/sinx and that the left ball must travel d in a certain amount of time. The equation v0=(d*g*tanx)^1/2 was derived and it was determined that the minimum value is at x=45 degrees, where v=(d*g)^1/2.
  • #1
mmmboh
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[PLAIN]http://img178.imageshack.us/img178/4781/345b.jpg

So I said v=v0-gt, and at the highest point, v=0, so t=v0/g.
I also said uy=u0sinx-gt, and ux=u0cosx.
So at t=v0/g, both balls have to be at their highest pint, and when uy=0, t=u0sinx/g...so equating the two times, I find u0sinx=v0...which I guess is obvious without calculation.
So uy0=v0, and ux0=v0cotx, and u0=v0/sinx.
In this time, the left ball must travel d, so ux0*t=v0cotx*v0/g=v02cotx/g=d...
I did some rearranging and found that v0=(d*g*tanx)1/2.
Since u0=v0/sinx=(d*g*tanx)1/2/sinx, we need to minimize (tanx)1/2/sinx= (1/(sinxcosx))1/2...which is a minimum at x=45o, and when x=45o, v=(d*g)1/2.
Is this right?
 
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Looks right to me.
 

FAQ: Two Balls Colliding. Check my work please

1. What is the definition of "Two Balls Colliding"?

The term "two balls colliding" refers to the physical phenomenon in which two objects, typically spherical in shape, come into contact with each other and transfer energy and momentum through the collision.

2. How do you calculate the speed and direction of the balls after the collision?

The speed and direction of the balls after the collision can be calculated using the principles of conservation of momentum and energy. This involves taking into account the masses and velocities of the balls before and after the collision.

3. What factors affect the outcome of two balls colliding?

There are several factors that can affect the outcome of two balls colliding, including the masses and velocities of the balls, the angle of collision, and the elasticity of the balls (how much they can deform and then return to their original shape).

4. Can the collision between two balls be perfectly elastic?

Yes, in theory, a collision between two balls can be perfectly elastic if there is no loss of kinetic energy during the collision. This would require the balls to be perfectly spherical and made of a perfectly elastic material.

5. How is the collision between two balls different from a collision between two objects of different shapes?

The main difference between a collision between two balls and a collision between two objects of different shapes is the distribution of mass and the contact area during the collision. This can affect the outcome of the collision and the calculation of the resulting speeds and directions of the objects.

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