The total momentum before and after the collision must be conserved.
- Let's start from the end: at this point, both cart and laundry bag are moving together, with a total mass of (m1+m2) and velocity 2.6 m/s. Therefore, the total momentum is
[tex]p_f = (m_1+m_2) v_f =(20 kg+8.3 kg)(2.6 m/s)=73.6 kg \cdot m/s[/tex]
- The momentum must be conserved, so the initial momentum must be equal to this value:
[tex]p_i = p_f = 73.6 kg \cdot m/s[/tex]
- At the beginning, the cart is stationary, so its momentum is zero. There is only one momentum, the one of the bag, which has a mass of 20 kg and unknwon velocity vi:
[tex]p_i = m_1 v_i[/tex]
- So, using the conservation of momentum we find
[tex]m_1 v_i = 73.6 kg \cdot m/s[/tex]
and from this, the initial velocity of the laundry bag:
[tex]v_i = \frac{p_f}{m_1}= \frac{73.6 kg \cdot m/s}{20 kg}=3.7 m/s [/tex]
