A boat sail 4km on the bearing 038 degree and then 5km on the bearing of 067 degree
How far is the boat from it starting point
Calculate the bearing of the boat from the starting point
To find the distance of the boat from its starting point, we can use the concept of vectors. We can break down the distance traveled into its horizontal and vertical components using trigonometry.
Let's start by finding the horizontal and vertical distances traveled:
Horizontal Distance:
The horizontal distance traveled is the sum of the horizontal components of both displacements.
For the first displacement of 4 km on a bearing of 038 degrees, the horizontal component is given by:
horizontal_1 = 4 km * cos(038°)
Next, for the second displacement of 5 km on a bearing of 067 degrees, the horizontal component is given by:
horizontal_2 = 5 km * cos(067°)
The total horizontal distance traveled is the sum of these two horizontal components:
horizontal_total = horizontal_1 + horizontal_2
Vertical Distance:
Similarly, the vertical distance traveled is the sum of the vertical components of both displacements.
For the first displacement, the vertical component is given by:
vertical_1 = 4 km * sin(038°)
And for the second displacement, the vertical component is given by:
vertical_2 = 5 km * sin(067°)
The total vertical distance traveled is the sum of these two vertical components:
vertical_total = vertical_1 + vertical_2
Now we can find the distance of the boat from its starting point using the Pythagorean theorem:
distance = √(horizontal_total^2 + vertical_total^2)
To calculate the bearing of the boat from the starting point, we can use trigonometry again. The bearing is the angle between the north line and the line connecting the starting point to the boat's position.
We can find the bearing by taking the inverse tangent of the vertical distance divided by the horizontal distance:
bearing = arctan(vertical_total / horizontal_total)
Now, substituting the values into the equations, let's compute the answer.