A car is heading northwest at 80 km/h and a truck is heading east at 60 km/h. Determine the velocity of the truck relative to the car.
Vrel = Vtruck - Vcar
That must be treated as a vector equation. Break it up into x (east) and y (north) components.
Vrel,x = 60 -80 sin45 = 3.4 km/h
Vrel,y = 0 - 80 cos 45 = -56.6 km/h
To determine the velocity of the truck relative to the car, we need to use vector addition.
The northwest direction can be represented by a vector pointing 45 degrees above the positive x-axis. The car's velocity vector can be represented as a vector with a magnitude of 80 km/h in the northwest direction.
The east direction can be represented by a vector pointing along the positive x-axis. The truck's velocity vector can be represented as a vector with a magnitude of 60 km/h in the east direction.
To find the relative velocity, we subtract the car's velocity vector from the truck's velocity vector.
First, let's break down the car's velocity vector into its components. The northwest direction is a combination of the north and west directions. Since northwest is 45 degrees above the positive x-axis, the north and west component vectors will have the same magnitude.
Using trigonometry, we can find the magnitude of the north and west components of the car's velocity vector:
magnitude of west component = 80 km/h * cos(45°)
magnitude of north component = 80 km/h * sin(45°)
Next, let's break down the truck's velocity vector into its components. Since the truck is moving only in the east direction, it does not have any north or west components.
Now, let's find the relative velocity by subtracting the car's velocity vector components from the truck's velocity vector components:
relative velocity in the x-direction = 60 km/h - 80 km/h * cos(45°)
relative velocity in the y-direction = 0 km/h - 80 km/h * sin(45°)
By substituting the values, we can calculate the relative velocity.