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 speed at which the center of mass is traveling, we need to apply the principle of vector addition.

The velocity of the first car moving east can be represented as (89.0 km/h, 0 km/h) since it is only moving in the x-axis direction.

Similarly, the velocity of the second car moving south can be represented as (0 km/h, -89.0 km/h) as it is only moving in the y-axis direction.

Now, we can add the two velocity vectors together:

(89.0 km/h, 0 km/h) + (0 km/h, -89.0 km/h) = (89.0 km/h, -89.0 km/h)

To find the magnitude of this resultant vector, we can use the Pythagorean theorem:

velocity = √(89.0 km/h)^2 + (-89.0 km/h)^2

velocity = √(7921 km^2/h^2 + 7921 km^2/h^2) = √(2 * 7921 km^2/h^2) = √(2) * 7921 km/h ≈ 112 km/h

Hence, the magnitude of the velocity of the center of mass of the two cars is approximately 112 km/h.

To find the speed (magnitude of velocity) at which the center of mass of the two cars is traveling, we can use the concept of vector addition.

Let's assume that the eastward direction is positive for convenience. The first car's velocity vector would be 89.0 km/h in the positive x-direction, while the second car's velocity vector would be 89.0 km/h in the negative y-direction.

To find the velocity of the center of mass, we can add the vectors of the two cars. The x-component of the resulting velocity vector would be the sum of the x-components (since the cars are moving in the same direction), and the y-component would be the sum of the y-components (since the cars are moving in opposite directions).

The x-component of the resulting velocity would be 89.0 km/h, and the y-component would be -89.0 km/h.

To find the magnitude (speed) of the velocity vector, we can use the Pythagorean theorem:

magnitude of velocity = √[(x-component)^2 + (y-component)^2]

magnitude of velocity = √[(89.0 km/h)^2 + (-89.0 km/h)^2]

magnitude of velocity = √[7921 km^2/h^2 + 7921 km^2/h^2]

magnitude of velocity = √[2 * 7921 km^2/h^2]

magnitude of velocity = √(15842 km^2/h^2)

magnitude of velocity ≈ 125.89 km/h

So, the center of mass of the two cars is traveling at a speed of approximately 125.89 km/h.