You walk 53 m to the north, then turn 60° to your right and walk another 45m. Determine the direction of your displacement vector. Express your answer as an angle relative to east.

To determine the direction of your displacement vector, we can use trigonometry.

First, let's break down the given information:

- You walk 53 m to the north. This means your initial displacement is 53 m in the north direction.

- Then, you turn 60° to your right. This means you are now facing east and need to find the additional displacement in this new direction.

- Finally, you walk another 45 m. This additional displacement is in the east direction.

To determine the total displacement vector, we can use the concept of vector addition. We can add the initial north displacement vector and the east displacement vector to get the result.

Using trigonometry, we can find the horizontal and vertical components of the east displacement vector:

Horizontal component: 45 m × cos(60°) = 45 m × 0.5 = 22.5 m

Vertical component: 45 m × sin(60°) = 45 m × 0.866 = 38.97 m

Now, let's find the total horizontal and vertical components:

Horizontal component: 0 + 22.5 m = 22.5 m

Vertical component: 53 m + 38.97 m = 91.97 m

To find the angle relative to east, we can use the inverse tangent function:

tan^-1(91.97 m / 22.5 m) ≈ 75.3°

Therefore, the direction of your displacement vector is approximately 75.3° relative to east.

To determine the direction of your displacement vector, we need to find the angle between the line that connects your starting point to your ending point, and the east direction. Here's how you can calculate it:

1. Start by drawing a diagram to visualize the situation. Draw a line segment that represents the 53 m to the north.
2. From the end of that line segment, draw another line segment that is 45 m long at a 60° angle to the right.
3. Now, draw a straight line from the starting point (where you began walking) to the end point (where you ended up after walking).
4. You should now have a triangle formed by the three line segments you drew.
5. To calculate the angle of displacement relative to east, we need to find the angle between the displacement vector and the east direction. The displacement vector is the line that connects the starting point to the end point.
6. Measure the angle between this displacement vector and the horizontal line that represents the east direction. You might need a protractor or an angle measuring tool to do this accurately.
7. Express the angle as a positive value relative to east. For example, if the angle measures 30° clockwise from east, you would express it as 30°. If the angle measures 45° counterclockwise from east, you would express it as -45°.

By following these steps, you can determine the direction of your displacement vector expressed as an angle relative to east.

Add the two displacement vectors. This will tell you the magnitude and direction of the resultant.

If you do not understand how to add vectors, I suggest a review or private tutoring in that subject.