Answer to Question #194837 in Physics for Wembly

Question

t an intersection, Car 1 with mass 1050 kg, going Eastward and Car 2 with mass 1870 kg, going Northward smash into each other as shown in Diagram P.

The two cars entangle and travel together after the collision, sliding at 17.5 m/s in the direction 25.00 East of North. The collision happens while it is raining therefore friction forces between the cars and the road are negligible. The speed of each car before the collision is

Answer 1

According to momentum conservation, the momenta along each axis are saved:

$$p_{Ei}=p_{Ef},\\ p_{Ni}=p_{Nf}.$$

The initial momentum $(p_i)$ correspond to the masses of the cars times their velocities, the final momentum is common mass of two cars times their velocities in respective direction:

$$p_{Ei}=m_Ev_E,\\ p_{Ef}=(m_E+m_N)u\sin25°,\\ p_{Ni}=m_Nv_N,\\ p_{Nf}=(m_E+m_N)u\cos25°.$$

Equate initial and final momentum:

$$1050v_E=(1050+1870)(17.5)\sin25°,\\ 1870v_N=(1050+1870)(17.5)\cos25°.\\ v_E=20.6\text{ m/s},\\ v_N=24.8\text{ m/s}.$$