Two cars leave a fork in a road at the same time. Car Q travels at 65 km/h to the west and car P travels at 95 km/h at 45° north of east. Calculate the relative velocity of car P with reference to car Q.
To calculate the relative velocity of car P with reference to car Q, we need to find the vector sum of their velocities.
Let's break down car P's velocity into its east and north components. The eastward component of car P's velocity is calculated as follows:
Eastward component = 95 km/h * cos(45°)
Eastward component = 95 km/h * 0.707
Eastward component = 67.215 km/h
The northward component of car P's velocity is calculated as follows:
Northward component = 95 km/h * sin(45°)
Northward component = 95 km/h * 0.707
Northward component = 67.215 km/h
Therefore, car P's velocity can be broken down as 67.215 km/h eastward and 67.215 km/h northward.
Now, let's find the relative velocity of car P with reference to car Q by subtracting the velocity of car Q from the velocity of car P:
Relative velocity = Velocity of P - Velocity of Q
Relative velocity = (67.215 km/h eastward + 67.215 km/h northward) - 65 km/h westward
Relative velocity = 67.215 km/h eastward + 67.215 km/h northward - 65 km/h westward
Relative velocity = 67.215 km/h eastward + 67.215 km/h northward + 65 km/h eastward
Relative velocity = 132.215 km/h eastward + 67.215 km/h northward
Therefore, the relative velocity of car P with reference to car Q is 132.215 km/h eastward and 67.215 km/h northward.