How will I know how the second ball will move?

[karlkue]

A ball rolls down, at an incline, and hits another ball, on a horizontal surface, in a certain angle, their masses are different. How do I solve for this? How will I know how the second ball will move?

 

[karlkue]

Please help me I need it very soon.

 

[tanujkush]

you can try using the conservation of momentum, if the surface on which the balls are kept frictionless. So what you need to do is that initial momentum of the system = final momentum of the system.

You'll have velocities in both x and y directions, since the first ball is coming at an angle. Just equate momentums in both x and y directions and you will be able to solve for the velocity of the second ball.

 

[RoyalCat]

tanujkush, he's missing an equation.

You have three variables, the velocity of ball #1 after the collision, the velocity of ball #2 after the collision, and the angle between the two.

Without an additional equation, you cannot solve this system of equations. If you were told mechanical energy is conserved (Completely elastic collision), then you would have another equation and you would be able to solve the problem.

Alternatively, if you knew the angle of dispersion, you could solve the equations just as well.

 

[tanujkush]

tanujkush, he's missing an equation.

You have three variables, the velocity of ball #1 after the collision, the velocity of ball #2 after the collision, and the angle between the two.

Without an additional equation, you cannot solve this system of equations. If you were told mechanical energy is conserved (Completely elastic collision), then you would have another equation and you would be able to solve the problem.

Alternatively, if you knew the angle of dispersion, you could solve the equations just as well.

Yeah I missed out the equation for conservation of energy! Sorry!

The angles though would be known (if one assumes a non dissipative collision, which I'm sure you've been told to assume)

 

[RoyalCat]

Yeah I missed out the equation for conservation of energy! Sorry!

The angles though would be known (if one assumes a non dissipative collision, which I'm sure you've been told to assume)

Now that I read more closely, he said that there's "a certain angle" so I think the angle is known in this case.

Anyway, the easiest way to approach this problem is, in my opinion, conservation of momentum using the law of cosines.

$$\vec P_i=\vec P_1'+\vec P_2'$$

Find what these three vectors are, and draw out them out, showing that the right hand side is equal to the left hand side. From there the application of the law of cosines is just a question of trigonometric insight. :)