a boat leaves shore and travels 30km east and then 15km 50 degree South of east Find the resultant the boats resultant displacement?

(30,0) + (9.64,-11.50) = (39.64,-11.50)

√(39.64^2 + 11.50^2) = 41.27
tanθ = -11.50/39.64

what is the wright solution

To find the resultant displacement of the boat, we need to use vector addition. Here are the steps:

Step 1: Represent the boat's displacement vectors graphically.
- Draw the first displacement vector of 30 km to the east.
- Draw the second displacement vector of 15 km at a 50-degree angle south of east.

Step 2: Break down the second displacement vector into its east and south components.
- The east component can be found using cosine: 15 km * cos(50°) ≈ 9.66 km.
- The south component can be found using sine: 15 km * sin(50°) ≈ 11.48 km.

Step 3: Add the east and south components to the first displacement vector.
- Add the east components: 30 km + 9.66 km = 39.66 km.
- Add the south components: 0 km (since there is no south component in the first displacement).

Step 4: Calculate the magnitude and direction of the resultant displacement.
- The magnitude of the resultant displacement is the distance between the starting point and the endpoint: √(39.66^2 + 11.48^2) ≈ 41.11 km.
- The direction of the resultant displacement can be found using tangent: tan⁻¹(11.48 km / 39.66 km) ≈ 16.8° south of east.

Therefore, the boat's resultant displacement is approximately 41.11 km at an angle of 16.8° south of east.

To find the resultant displacement of the boat, we can use vector addition.

First, let's draw a diagram to visualize the boat's movement.

Start by drawing a line going 30 km east. Then, draw another line at a 50-degree angle south of the eastward direction. This line should be 15 km long.

Now, let's break down these vectors into their components.

The eastward vector has no vertical component, so its horizontal component is 30 km.

To find the components of the southward vector, we use trigonometry. The angle between the southward vector and the horizontal axis is 90 degrees (since it is directly south), minus the given 50 degrees.

The vertical component is calculated as follows:
Vertical component = 15 km * sin(90 - 50)

The horizontal component is calculated as follows:
Horizontal component = 15 km * cos(90 - 50)

Now, we can add up the horizontal components and the vertical components separately.

Horizontal component sum = 30 km + 15 km * cos(90 - 50)
Vertical component sum = 15 km * sin(90 - 50)

Finally, we can find the magnitude (resultant) of the displacement vector using the Pythagorean theorem.

Resultant displacement = √(Horizontal component sum^2 + Vertical component sum^2)