a ship, leaving its port, sails due north for 45.0km and then 60.0km in a direction 60o east of north. determine the location of the ship relative to the port.
magnitude=102km
Direction= 73 degrees
magnitude= 102km due East of North**
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To determine the location of the ship relative to the port, we need to break down the distances traveled into their north and east components.
First, let's consider the 45.0km distance traveled due north. Since the ship is moving directly north, there is no eastward displacement in this segment. Therefore, the ship's northward displacement is 45.0km, and its eastward displacement is 0km.
Next, let's examine the 60.0km distance traveled in a direction 60 degrees east of north. To find the north and east components of this distance, we need to use trigonometry.
The northward displacement can be calculated using the sine function: north displacement = distance * sin(angle). So the north displacement is 60.0km * sin(60°) = 51.96km.
The eastward displacement can be calculated using the cosine function: east displacement = distance * cos(angle). So the east displacement is 60.0km * cos(60°) = 30.00km.
Now, we can determine the total north and east displacements by adding up the values from both segments:
Total north displacement = 45.0km + 51.96km = 96.96km
Total east displacement = 0km + 30.00km = 30.00km
Finally, we can use these displacements to determine the location of the ship relative to the port. The ship's location can be represented in vector form as (east displacement, north displacement), so the ship's location relative to the port is (30.00km, 96.96km).