a ship leaves port with a bearing of S 42deg W after traveling 7 miles, the ship turns 90deg and travels on a bearing of N 52deg W for 10 miles at that time, what is the bearing of the ship to the port?
Hmm. You, NATO and Selena ought to be able to figure this out if you put your heads together...
To determine the bearing of the ship to the port, we can use the concept of vector addition. Let's break down the given information step by step:
1. The ship leaves the port with a bearing of S 42° W. This means that the initial direction of the ship is towards the south-west from the port.
2. After traveling 7 miles, the ship makes a turn of 90°. This means the ship changes its direction from south-west to north-west.
3. The ship then travels on a bearing of N 52° W for 10 miles. This means the ship is moving towards the northwest direction but slightly towards the north.
Now, let's calculate the final bearing of the ship to the port:
1. Convert the given bearings into Cartesian coordinate form, where positive x-axis is east and positive y-axis is north.
- Bearing S 42° W:
angle = 90° - 42° = 48°
x-component = -7 * sin(48°)
y-component = -7 * cos(48°)
So, the vector for the initial movement is (x1, y1) = (-7 * sin(48°), -7 * cos(48°))
- Bearing N 52° W:
angle = 90° + 52° = 142°
x-component = 10 * sin(142°)
y-component = 10 * cos(142°)
So, the vector for the second movement is (x2, y2) = (10 * sin(142°), 10 * cos(142°))
2. Add the two vectors to get the resultant vector:
x-component = x1 + x2
y-component = y1 + y2
3. Calculate the magnitude and direction of the resultant vector:
magnitude = sqrt((x-component)^2 + (y-component)^2)
direction = arctan((y-component) / (x-component))
4. Convert the direction angle into a bearing angle:
- If the direction angle is positive, add 90° to it and subtract from 360°.
- If the direction angle is negative, add 90° to it.
This will give us the bearing angle from the north (clockwise).
Hence, by following these steps, you can calculate the final bearing of the ship to the port.