A car is driven 165 km west and then 25 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

Since no starting point was given, I assumed the trip started at the Origin.

Therefore, we'll subtract 0 from the vector sum to get the displacement.

Southwest = 45 deg. west of South = 225 deg CCW from 0 deg.

X = Hor. = -165 + 165*cos225,
X = -165 + -17.7 = -182.7 km,

Y = Ver. = 25*sin225 = -17.7 km.

tanA = 17.7 / 182.7 = 0.0969,
A = 5.53 deg,

D = 182.7 + i17.7,
D = 182.7 / cos5.53 = 183.6 km @
5.53 deg South of West.

D = 182.7 +i17.7,

CORRECTION!

X = Hor. = -165 + 25*cos225.

To find the displacement of the car, we need to calculate the vector sum of the two displacements: 165 km west and 25 km southwest.

First, let's convert the southwest displacement into its components.

- The southwest displacement can be broken down into two parts: a horizontal component (westward) and a vertical component (southward).
- The horizontal component is given by a right-angled triangle, with a hypotenuse of 25 km and an angle of 45 degrees (45 degrees is the angle between southwest and west).
- To find the horizontal component, we can use trigonometry. The horizontal component (westward) can be found using the equation: horizontal component = hypotenuse * cos(angle).
- In this case, the horizontal component is 25 km * cos(45 degrees) = 25 km * 0.707 ≈ 17.68 km.

Now, let's calculate the total displacement by adding the two displacements together.

- Since the west displacement is purely horizontal, the total horizontal displacement is 165 km to the west.
- The total vertical displacement is the sum of the vertical components of both displacements, which is 0 km (since the southwest displacement has no north-south component).
- Therefore, the total displacement is 165 km to the west horizontally and 0 km vertically.

Lastly, let's calculate the magnitude and direction of the displacement.

- The magnitude (or length) of the displacement can be found using the Pythagorean theorem. It is the square root of the sum of the squares of the horizontal and vertical displacements.
- In this case, the magnitude of the displacement is √((165 km)^2 + (0 km)^2) = √(27225 km^2) ≈ 165 km.
- The direction of the displacement is the direction with respect to a reference point (usually north). In this case, since the displacement is purely westward, the direction would be west.

So, the displacement of the car from the point of origin is approximately 165 km westward.