- #1
Saladsamurai
- 3,009
- 7
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!
