What is the final velocity of the two balls in an elastic collision?

[Saladsamurai]

Homework Statement

I can't believe I cannot get this! I am trying to help out my gf with this problem:

A 5 kg ball moving at 2 m/s to the right collides with a 7.5 kg stationary ball. If the collision is elastic, what are the final velocities of the 2 balls?

Homework Equations

Momentum is Conserved
KE is conserved

The Attempt at a Solution

Momentum

$(m_1v_1)_o+(m_2v_2)_o = (m_1v_1)_f+(m_2v_2)_f$

$\Rightarrow (5)(2) + (7.5)(0) = 5v_{1f} + 7.5v_{2f}$

$v_{1f} = 2 - 1.5v_{2f} \qquad (1)$

Energy

$0.5(m_1v_1^2)_o+0.5(m_2v_2^2)_o = 0.5(m_1v_1^2)_f+0.5(m_2v_2^2)_f$

$\Rightarrow (5)(2)^2 = 5v_{1f}^2 + 7.5v_2f}^2$

$$v_{1f} = \sqrt{4 - 1.5v_{2f}^2} \qquad (2)$$


From (1) and (2), we have

$$2 - 1.5v_{2f} = \sqrt{4 - 1.5v_{2f}^2}$$

$\Rightarrow 4 - 3v_{2f} + 2.25v_{2f}^2 = 4 - 1.5v_{2f}$

$\Rightarrow 3.75v_{2f}^2 - 3v_{2f} = 0 = (3.75v_{2f} - 3)v_{2f}$

$\Rightarrow v_{2f} = 0.8 m/s$

Which is incorrect.

What the heck am I missing? I feel like such an amateur right now!

 

[Elvex]

It's a simple arithmetic mistake... you didn't square the binomial correctly in...

(2 - 1.5v_2f) ^ 2

the cross term is -6v_2f not -3v_2f.

 

[Saladsamurai]

It's a simple arithmetic mistake... you didn't square the binomial correctly in...

(2 - 1.5v_2f) ^ 2

the cross term is -6v_2f not -3v_2f.

Oh jeesh...thank you Elvex!