Question

A 1-kg object moving at 1 m/s undergoes a one-dimensional elastic collision with a 2-kg object initially at rest. What is the speed of the 1-kg object after the collision?

Answer 1

$m_1 = 1 \;kg \\ u_1 = 1 \;m/s \\ m_2 = 2 \;kg \\ u_2 = 0 \;m/s$

Final speed of the object (1):

$v_1 = \frac{m_1-m_2}{m_1+m_2} \times u_1 + \frac{2m_2}{m_1+m_2} \times u_2 \\ = \frac{1-2}{3} \times 1 + \frac{2 \times 2}{3} \times 0 \\ = -\frac{1}{3} \\ = -0.33 \;m/s$

Negative sign shows direction.

Answer: 0.33 m/s