Two cars leave the same point at the same time, each travelling at the same constant speed of 89.0 km/h and each having the same mass. However, the first car drives directly east, while the second car heads directly south. At what speed (the magnitude of the velocity) is the centre of mass of these two cars travelling? Give your answer as a positive value in km/h (without a sign).
To find the velocity of the center of mass, we need to consider the relative velocities of the two cars. Since the cars are moving in perpendicular directions (east and south), we can use the Pythagorean theorem to find the magnitude of the resultant velocity.
Let's break down the velocities of the two cars:
1. The first car is traveling directly east at a constant speed of 89.0 km/h. This means its velocity vector can be represented as (89.0 km/h, 0 km/h).
2. The second car is traveling directly south at a constant speed of 89.0 km/h. This means its velocity vector can be represented as (0 km/h, -89.0 km/h).
Now, we can find the resultant velocity by using the Pythagorean theorem:
Resultant velocity = sqrt((89.0 km/h)^2 + (-89.0 km/h)^2)
Calculating this equation will give us the magnitude of the velocity of the center of mass.
Resultant velocity = sqrt(7921 km^2/h^2 + 7921 km^2/h^2)
Resultant velocity ≈ sqrt(15842 km^2/h^2)
Resultant velocity ≈ 125.98 km/h
Therefore, the center of mass of these two cars is moving at a speed of approximately 125.98 km/h.