A car with a mass of 1,260 kg traveling south strikes a Semi with a mass of 8,500 kg that is heading west. The vehicles stick together and move southwest at a 12 degree angle at 21.380 km/hr. How fast were the vehicles traveling (no friction).

Question

matt101 · Answer

This is a conservation of momentum question. The trick here is that you need to consider momentum in two dimensions: north/south and east west. When the car and semi collide, they move diagonally, but you can deconstruct this into north/south ("vertical") and east/west ("horizontal") components. If you draw out the situation, you'll find that the vertical component of the momentum is psinθ, while the horizontal component is pcosθ. Note that p=(m+M)v(f), where m is the mass of the car, M is the mass of the semi, and v(f) is the final velocity of the two together after colliding.

Now we can set up some equations. In the vertical direction, the initial momentum of the car must equal the final vertical momentum of the car+semi:

$$mv_{m_i}=(m+M)v_f \sin \theta$$
In the horizontal direction, the initial momentum of the semi must equal the final momentum of the car+semi in the east/west direction:

$$Mv_{M_i}=(m+M)v_f \cos \theta$$
In both of these equations, you are given all the information in the question except for the initial velocities of the car/semi. Plug in what you're given and solve!

anonymous · Answer

Thanks, u r a genius