One and Two Dimension collisions

[clippers0319]

My question is not so much what to do it is just i have problems solving for a certain equation.

A 5.00kg ball, moving to the right at a velocity of 2m/s on a frictionless table, collides head-on with a stationary 7.50kg ball. Find the final velocities of the balls if the collision is (a) elastic and (b) completely inelastic

for part A

I have m1v1f + m2v2f= m1vi1 +0
to solve for final velocity 1(the ball for 5kg) you use

vf1=(m1-m2/m1+m2)vi1

I really have no i do how to algebraically solve for vf1, can someone explain that to me because when i use the equation i get the right answer which is -.400m/s

To find vf2 we use the fact that it is an ellastic collision and the kinetic energy before and after is the same

1/2m1(vf1^2)+1/2m2(vf2^2)=1/2m1(vi1^2)+0
Using this i have to solve for vf2 but again i have a problem algebraically solving for vf2. But there is a similar example in the textbook so i used what they had to solve for vf1 and vf2 but they do not show the work

vf2=(2m1/m1+m2)vi1
answer should be 1.60m/s

Same problem here but the answers come out correctly.
It would be greatly appreciated if someone can show me the algebra behind this

 

[radou]

For (a): use the fact that both kinetic energy and momentum are conserved. This will give you two equations with two unknowns, which are the final velocities.

For (b): what are the properties of a completely inelastic collision?

 

[clippers0319]

I understand that but i need someone to show me how to algebraically solve for those two equations that's what my problem is i understand how to solve for the final velocities. Like show the math workout step by step because i am confused.

 

[radou]

I understand that but i need someone to show me how to algebraically solve for those two equations that's what my problem is i understand how to solve for the final velocities. Like show the math workout step by step because i am confused.

Here, take a look at: http://www.webmath.com/solver2.html" .