Dont understand this momentum problem

[physicskid72]

Homework Statement

Two air track gliders of a mass 300 g and 200 g are moving towards each other in opposite directions with speeds of 50 cm/s and 100cm/s respectively. Take the direction of the more massive glider as positive.

A.) determine the velocity of each glider after the collision if the collision is elastic.

Homework Equations

m1v1i +m2v2i = m1v1f + m2v2f

quoted by "collinsmark" - "You have enough information to solve it (given that this is a 1 dimensional problem -- things can get more complicated if the objects can freely move in more than 1 dimension)."

"You have the conservation of momentum equation that you listed above. But since you are assuming it is a perfectly elastic collision, you can also use conservation of kinetic energy (conservation of kinetic energy only applies if the collision is perfectly elastic). So you have 2 equations and 2 unknowns, which is solvable."

The Attempt at a Solution

I know collinsmark was right in what he is saying but i don't undrstand what formuals to use to get the separate velocites.

Like this?

3(0.50) + 0.2(-1.00) = 0.3v1f
3(0.50) + 0.2(-1.00) = 0.2v2f

then solve for the separate velocites in each case?

or just m1v1i = m1v1f
so the velocity doesn't change only in direction.

any help is greatly appreciated.

 

[rock.freak667]

The Attempt at a Solution

I know collinsmark was right in what he is saying but i don't undrstand what formuals to use to get the separate velocites.

Homework Equations

m1v1i +m2v2i = m1v1f + m2v2f

This is conservation of momentum, so this is one equation.

Next you have an elastic collision, meaning initial kinetic energy = final kinetic energy, this will give you another equation. Now you can solve these two equations for the velocities.

 

[PhanthomJay]

You had the first equation you need ,correct, in the previous post; now you're getting it messed up. You didn't take collinsmark's advice about the second equation you need to solve (a bit tediously) for the 2 unknowns . You should go back to that original post post and seek additional help there.

 

[physicskid72]

i know the two equations are

m1v1i +m2v2i = m1v1f + m2v2f

and

1/2(m1)(v1i)^2 + 1/2(m2)(v2i)^2 = 1/2(m1)(v1f)^2 + 1/2(m2)(v2f)^2

or

KEi = KEf

I'm just not sure how to solve for the individual velocities.

 

[rock.freak667]

i know the two equations are

m1v1i +m2v2i = m1v1f + m2v2f

and

1/2(m1)(v1i)^2 + 1/2(m2)(v2i)^2 = 1/2(m1)(v1f)^2 + 1/2(m2)(v2f)^2

Right, it's easier to plug in the numbers than to deal with all of the symbols, but when you plug in the numbers, try gathering the like terms on one side of each equation.

 

[physicskid72]

it is still vague, do i combine the two equations? i mean if you simply rearrange you end up with two variables to solve for so you must have to use a combined formula right?

 

[rock.freak667]

it is still vague, do i combine the two equations? i mean if you simply rearrange you end up with two variables to solve for so you must have to use a combined formula right?

take the first equation, make one variable the subject and substitute it into the other equation.