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Answer:
The magnitude of the boat's velocity is 8.21 km/h.
Explanation:
We can find the boat's velocity as follows:
[tex] \Epsilon V_{x} = V_{w_{x}} + V_{b_{y}} [/tex]
[tex] \Epsilon V_{y} = V_{w_{y}} + V_{b_{y}} [/tex]
Where:
[tex]V_{w_{x}}[/tex] and [tex]V_{w_{y}}[/tex] are the components of the velocity of the water in the x and y-direction
[tex]V_{b_{x}}[/tex] and [tex]V_{b_{y}}[/tex] are the components of the velocity of the boat in the x and y-direction
Since the angle is 15° we have:
[tex] \Epsilon V_{x} = -4.0 km/h*sin(15) + 0 = -1.04 km/h [/tex]
[tex] \Epsilon V_{y} = 4.0 km/h*cos(15) - 12.0 km/h = -8.14 km/h [/tex]
Now, the velocity of the boat is:
[tex] V = \sqrt{V_{x}^{2} + V_{y}^{2}} = \sqrt{(-1.04 km/h)^{2} + (-8.14 km/h)^{2}} = 8.21 km/h [/tex]
Therefore, the magnitude of the boat's velocity is 8.21 km/h.
I hope it helps you!