Answer:
a) 9.6 m/s
b) 11.7 m/s
c) 12 m/s
Explanation:
This problem can be solved by the Conservation of Momentum principle, which establishes that the initial momentum [tex]p_{o}[/tex] must be equal to the final momentum [tex]p_{f}[/tex]:
[tex]p_{o}=p_{f}[/tex] (1)
Where:
[tex]p_{o}=m_{g} V_{o} + m_{b} U_{o}[/tex] (2)
[tex]p_{f}=m_{g} V_{f} + m_{b} U_{f}[/tex] (3)
[tex]m_{g}=0.5 kg[/tex] is the mass of green ball
[tex]m_{b}=0.5 kg[/tex] is the mass of the blue ball
[tex]V_{o}=12 m/s[/tex] is the initial velocity of the green ball
[tex]U_{o}=0 m/s[/tex] is the initial velocity of the blue ball
[tex]V_{f}[/tex] is the final velocity of the green ball
[tex]U_{f}[/tex] is the final velocity of the blue ball
Substituting (2) and (3) in (1):
[tex]m_{g} V_{o} + m_{b} U_{o}=m_{g} V_{f} + m_{b} U_{f}[/tex] (4)
Isolating [tex]U_{f}[/tex]:
[tex]U_{f}=\frac{m_{g} V_{o} - m_{g} V_{f}}{m_{b}}[/tex] (5)
[tex]U_{f}=\frac{m_{g} (V_{o} - V_{f})}{m_{b}}[/tex] (6) This is the equation we will use for the next cases
Knowing this, let's begin with the answers:
a) In this case [tex]V_{f}=2.4 m/s[/tex] and we have to find [tex]U_{f}[/tex]
[tex]U_{f}=\frac{0.5 kg (12 m/s - 2.4 m/s)}{0.5 kg}[/tex] (7)
[tex]U_{f}=9.6 m/s[/tex] (8)
b) In this case [tex]V_{f}=0.3 m/s[/tex] and we have to find [tex]U_{f}[/tex]
[tex]U_{f}=\frac{0.5 kg (12 m/s - 0.3 m/s)}{0.5 kg}[/tex] (9)
[tex]U_{f}=11.7 m/s[/tex] (10)
c) In this case [tex]V_{f}=0 m/s[/tex] and we have to find [tex]U_{f}[/tex]
[tex]U_{f}=\frac{0.5 kg (12 m/s - 0 m/s)}{0.5 kg}[/tex] (11)
[tex]U_{f}=12 m/s[/tex] (12)
