Two cars leave the same point at the same time, each travelling at the same constant speed and each having the same mass. The first car drives directly east, while the second car heads directly north. If the centre of mass of the two-car system is travelling at 51 km/h (i.e. the magnitude of the velocity), how fast is each car travelling in km/h?

93.0 km/h

To find the speed of each car, we can apply the principle of conservation of momentum. The center of mass velocity is given by:

\(V_{cm} = \frac{{m_1 V_1 + m_2 V_2}}{{m_1 + m_2}}\),

where \(m_1\) and \(m_2\) are the masses of the two cars, and \(V_1\) and \(V_2\) are their respective velocities.

Since both cars have the same mass, we can simplify the equation to:

\(V_{cm} = \frac{{2m V}}{{2m}} = V\),

where \(V\) represents the speed of both cars.

Given that \(V_{cm} = 51\) km/h, we can conclude that \(V = 51\) km/h.

Therefore, each car is traveling at a speed of 51 km/h.