Answer: 3.5 m/s
Explanation:
This problem can be solved by the Conservation of Momentum principle which establishes the initial momentum [tex]p_{i}[/tex] must be equal to the final momentum [tex]p_{f}[/tex], and taking into account this is an inelastic collision:
Before the collision:
[tex]p_{i}=mV_{o}+MU_{o}[/tex] (1)
After the collision:
[tex]p_{f}=(m+M)V_{f}[/tex] (2)
Where:
[tex]m=7 kg[/tex] is the mass of the first cart
[tex]V_{o}=9 m/s[/tex] is the velocity of the first cart
[tex]M=11 kg[/tex] is the mass of the second cart
[tex]U_{o}=0 m/s[/tex] is the velocity of the second cart
[tex]V_{f}[/tex] is the final velocity of both carts
[tex]p_{i}=p_{f}[/tex] (3)
[tex]mV_{o}+MU_{o}=(m+M)V_{f}[/tex] (4)
Since [tex]U_{o}=0 m/s[/tex]:
[tex]mV_{o}=(m+M)V_{f}[/tex] (5)
[tex]V_{f}=\frac{mV_{o}}{m+M}[/tex] (6)
[tex]V_{f}=\frac{(7 kg)(9 m/s)}{7 kg + 11 kg}[/tex] (7)
Finally:
[tex]V_{f}=3.5 m/s[/tex]
