Suppose you walk 18.0m straight west and then 25.0 m straight north. How far are you from your starting point and what is the compass direction of a line connecting your starting point to your final position>

Draw a diagram. Your trip forms the legs of a right triangle with legs 18 and 25.

So, the final displacement is √(18^2+25^2) = 30.8

The angle θ is such that
tanθ = 25/-18 = 125.75° or -234.25°

The compass bearing is 90°-θ = 324.25°
(360-35.75)°

Find the components of Vtot along the x and y axes where 0= 20.0 and Vtot= 5.52m/s

To find the distance from your starting point to your final position, we can use the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the 18.0m distance west and 25.0m distance north form the two sides of a right triangle. Let's call the distance from the starting point to the final position "d".

Using the Pythagorean theorem, we can find "d":

d^2 = (18.0m)^2 + (25.0m)^2

d^2 = 324m^2 + 625m^2

d^2 = 949m^2

Taking the square root of both sides, we find:

d ≈ √949m

d ≈ 30.8m

So, you are approximately 30.8 meters away from your starting point.

To find the compass direction of the line connecting your starting point to your final position, we can use trigonometry. Since we have a right triangle, we can use the tangent function to find the angle.

Let's call the angle "θ". The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

tan(θ) = (25.0m / 18.0m)

θ ≈ tan^(-1)(25.0m / 18.0m)

θ ≈ tan^(-1)(1.39)

θ ≈ 54.5°

So, the compass direction of the line connecting your starting point to your final position is approximately 54.5° north of west.

To find the distance and the compass direction from the starting point to the final position, we can use the Pythagorean theorem and trigonometric functions.

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

|\
| \
| \
| \
| \
| \
|________\

Let's label the starting point as "A," and the final position as "B."

Now, we'll calculate the distance using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

To use this theorem, we need to find the lengths of the vertical and horizontal sides of the triangle formed by your movement.

The vertical side (north) measures 25.0 m, and the horizontal side (west) measures 18.0 m.

Applying the Pythagorean theorem:

Distance^2 = 18.0^2 + 25.0^2

Distance^2 = 324.0 + 625.0

Distance^2 = 949.0

Taking the square root of both sides:

Distance ≈ √949.0

Distance ≈ 30.81 m

So, the distance from the starting point to the final position is approximately 30.81 meters.

Next, we'll determine the compass direction of the line connecting your starting point (A) to your final position (B).

To find the compass direction, we can use trigonometry. The tangent (tan) of an angle is equal to the opposite side divided by the adjacent side. In this case, the angle we're interested in is the one between the line connecting the starting point and the final position (AB) and the horizontal axis.

Let's call this angle θ.

We can find θ using the inverse tangent (arctan) function:

θ = arctan(opposite/adjacent)

θ = arctan(25.0/18.0)

θ ≈ 53.1°

So, the compass direction is approximately 53.1° north of west.