A 3.0-kg object moving in the positive x direction has a one-dimensional elastic collision with a 5.0-kg object initially at rest. After the collision the 5.0-kg object has a velocity of 6.0 m/s in the positive x direction. What was the initial speed of the 3.0 kg object?
A) 6.0 m/s
B) 7.0 m/s
C) 4.5 m/s
D) 8.0 m/s
E) 5.5 m/s

Question

Quizplus · Accepted Answer

Using conservation of momentum:
Initial momentum = Final momentum
$m_1v_1 + m_2v_2 = m_1v_{1f} + m_2v_{2f}$
where
$m_1 = 3.0$ kg
$m_2 = 5.0$ kg
$v_2 = 0$ m/s (initially at rest)
$v_{2f} = 6.0$ m/s (after collision)
We need to find $v_1$ (initial velocity of 3.0-kg object).
Rearranging the equation and solving for $v_1$:
$v_1 = \frac{m_2(v_{2f}-v_2)+m_1v_1}{m_1}$
Substituting values:
$v_1 = \frac{5.0(6.0-0)+3.0v_1}{3.0}$
$v_1 = 8.0$ m/s

A 30-Kg Object Moving in the Positive X Direction Has a a One-Dimensional