a car moves 20km towards north then 35km angle of 60 degree west of north.Determine the magnitude of displacement from initial point.

Add the two vectors. I recommend adding north (y) and east (+x) components

You end up with y coordinate
y = 20 + 35 cos 60
and x ccordinate
x = -35 sin 60

The displacement magnitude is
sqrt (x^2 + y^2)

I leave you to compute that number

To determine the magnitude of displacement from the initial point, we need to find the distance between the starting point and the final point. We can break down the car's movement into two components: the northward movement and the westward movement.

1. Northward movement: The car moves 20 km towards the north.

2. Westward movement: The car moves 35 km at an angle of 60 degrees west of north.

To find the westward component of the car's movement, we can use trigonometry. The cosine function relates the given angle to the adjacent side (westward component) and the hypotenuse (total displacement).

Cosine(60 degrees) = Adjacent side (westward component) / Hypotenuse (total displacement).

Cos(60 degrees) = x / 35 km.

x = 35 km * cos(60 degrees).

x = 35 km * (0.5).

x = 17.5 km (approx).

The westward component of the car's movement is approximately 17.5 km.

Now, we can find the total displacement by using the Pythagorean theorem, which states that the square of the hypotenuse (total displacement) is equal to the sum of the squares of the two sides (northward and westward components).

Total displacement^2 = Northward component^2 + Westward component^2.

Total displacement^2 = (20 km)^2 + (17.5 km)^2.

Total displacement^2 = 400 km^2 + 306.25 km^2.

Total displacement^2 = 706.25 km^2.

Taking the square root of both sides,

Total displacement = √706.25 km^2.

Total displacement ≈ 26.57 km.

Therefore, the magnitude of the car's displacement from the initial point is approximately 26.57 km.