a ship leaves a port and travels on asteady course 40*N of due east at a steady speed of 8.kmh^-1. how far due north and due east of the port is the ship after sailing after 12 hours

N=8*sin40*12

E=8*cos40*12

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To find the distance due north and due east, we can use the formula:

Distance = Speed × Time

Given:
Speed = 8 km/h
Time = 12 hours

Distance due east = Speed × Time
Distance due east = 8 km/h × 12 hours
Distance due east = 96 km

Therefore, the ship is 96 km due east of the port.

Distance due north is given by the formula:

Distance due north = Distance × sin(angle)

The angle is 40° north of due east, which means it forms a right angle triangle with the hypotenuse being the distance due east and the angle opposite the distance due north.

Using trigonometry:

Distance due north = 96 km × sin(40°)
Distance due north ≈ 61.01 km

Therefore, the ship is approximately 61.01 km due north of the port.

To summarize:
- The ship is 96 km due east of the port.
- The ship is approximately 61.01 km due north of the port.

To find the distance due north and due east of the port, we need to calculate the components of the ship's displacement.

First, let's find the distance traveled by the ship after 12 hours. Since the ship's speed is 8 km/h, we can use the formula:

Distance = Speed x Time

Distance = 8 km/h x 12 hours = 96 km

Now, let's break this displacement into its north and east components. Since the ship is traveling 40° north of due east, we can use trigonometry to find these components.

The north component can be found using the formula:

North Distance = Distance x sin(angle)

North Distance = 96 km x sin(40°)

Using a calculator, we find that sin(40°) ≈ 0.6428. Plugging in this value, we get:

North Distance ≈ 96 km x 0.6428 ≈ 61.77 km (rounded to two decimal places)

The east component can be found using the formula:

East Distance = Distance x cos(angle)

East Distance = 96 km x cos(40°)

Using a calculator, we find that cos(40°) ≈ 0.7660. Plugging in this value, we get:

East Distance ≈ 96 km x 0.7660 ≈ 73.70 km (rounded to two decimal places)

Therefore, after sailing for 12 hours, the ship is approximately 61.77 km due north and 73.70 km due east of the port.