Question

A 1200-kg car is travelling east at a rate of 9 m/s. A 1600-kg truck is travelling south at a rate of 13 m/s. The truck accidentally runs a stop sign and collides with the car in a completely inelastic collision. What is the speed of the combined mass after the collision?

Answer 1

Generally, we analyze the problem of collisions with the help of

1) Conservation of Mechanical Energy

2) Conservation of Linear Momentum

Now, since here the collision is inelastic in nature so

i) the forces are non-conservative

ii) As a result, the total kinetic energy is not conserved

The key point is that although the (kinetic) energy might not be conserved, the momentum is still conserved

For the case of completely inelastic collision, since the objects stick together they have the same final velocity.

Now, from the conservation of linear momentum, we can say that,

  

Now,   

Now, after collision let the combined mass forms an angle with the south of east.

So, finally we can write

So, on equating the x-component and y-component.we get

So, by dividing (2) by (1), we get

So,from (2)