Answer:
The final velocity of the skier and boat is 0.33 m/s to the east.
Explanation:
We can find the final velocity of the skier by conservation of linear momentum:
[tex] m_{s}v_{s_{i}} + m_{b}v_{b_{i}} = m_{s}v_{s_{f}} + m_{b}v_{b_{f}} [/tex]
Where:
[tex]m_{s}[/tex]: is the mass of the water skier = 62.0 kg
[tex]m_{b}[/tex]: is the mass of the boat = 775 kg
[tex]v_{s_{i}}[/tex]: is the initial velocity of the skier = 4.50 m/s (as she leaves the dock)
[tex]v_{b_{i}}[/tex]: is the initial velocity of the boat = 0 (it is at rest)
[tex]v_{s_{f}}[/tex]: is the final velocity of the skier =?
[tex]v_{b_{f}}[/tex]: is the final velocity of the boat =?
Since the final velocity of the skier is the same that the velocity of the boat ([tex]v_{f}[/tex]) we have:
[tex] m_{s}v_{s_{i}} + 0 = v_{f}(m_{s} + m_{b}) [/tex]
[tex]v_{f} = \frac{m_{s}v_{s_{i}}}{m_{s} + m_{b}} = \frac{62.0 kg*4.50 m/s}{62.0 kg + 775 kg} = 0.33 m/s
Therefore, the final velocity of the skier and boat is 0.33 m/s to the east.
I hope it helps you!
