a 4.50 kg mass traveling east at 5.0 m/s has a head-on elastic collision with a 1.5 kg mass traveling west at 3.0 m/s. find the velocity of each mass after the collision.

my work so far:
vif= (4.50-1.5/4.50 + 1.5) x2
v2f= (2m1/4.50+1.5) x 2
I don't get the right answer when I use these formulas, and I wondering what the correct formulas would be......and maybe show the plugging in of the numbers in the formulas if possible?

To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.

Step 1: Calculate the initial momentum of each mass separately.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v).
For the 4.50 kg mass traveling east: p1 = m1 * v1 = 4.50 kg * 5.0 m/s = 22.5 kg·m/s
For the 1.5 kg mass traveling west: p2 = m2 * v2 = 1.5 kg * (-3.0 m/s) = -4.5 kg·m/s (negative sign indicates opposite direction)

Step 2: Apply the conservation of momentum.
In an elastic collision, the total momentum before and after the collision is conserved.
The total initial momentum (p1 + p2) will equal the total final momentum (p1' + p2'), where p1' and p2' represent the final momenta of the masses.

Step 3: Apply the conservation of kinetic energy.
For an elastic collision, the total kinetic energy before and after the collision is conserved.
The total initial kinetic energy (KE1 + KE2) will equal the total final kinetic energy (KE1' + KE2'), where KE1' and KE2' represent the final kinetic energies of the masses.

Step 4: Solve for the final velocities.
We have two equations from the conservation of momentum and conservation of kinetic energy. By solving these equations simultaneously, we can find the final velocities.

Applying these principles to the given problem:

Let v1' and v2' be the final velocities of the 4.50 kg and 1.5 kg masses, respectively.

Conservation of momentum equation:
p1 + p2 = p1' + p2'
(4.50 kg * 5.0 m/s) + (1.5 kg * (-3.0 m/s)) = 4.50 kg * v1' + 1.5 kg * v2'

Conservation of kinetic energy equation:
(0.5 * 4.50 kg * (5.0 m/s)^2) + (0.5 * 1.5 kg * (-3.0 m/s)^2) = (0.5 * 4.50 kg * v1'^2) + (0.5 * 1.5 kg * v2'^2)

Simplifying and solving this system of equations will give you the final velocities v1' and v2'.

east momentum positive

initial
4.5 * 5 - 1.5 * 3 = 18

final
4.5 V1f + 1.5 V2f = 18

now energy (elastic means same before and after) (never happen:)

initial
(1/2)4.5(25) + (1/2)1.5(9)
= 63 Joules
after
(1/2)4.5(V1f)^2 + (1/2)1.5(V2f^2) = 63

there you have 2 equations and two unknowns
substitute
V2f = (18 - 4.5 V1f)/1.5
into your energy equation and solve