Car Crash problem?

Question

Two vehicles A and B are traveling west and south, respectively, toward the same intersection where they collide and lock together. Before the collision A (total weight 1170 N) is moving with a speed of 50 m/s and B (total weight 2710 N ) has a speed of 41 m/s.

What is the direction of motion of the interlocked vehicles immediately after the collision?

Answer 1

Use conservation of momentum in the x and y directions.

The mass of vehicle A is 119.4kg, the mass of vehicle B is 276.5kg. After the collision, the total mass of the vehicles is 395.9kg.

So conservation of momentum in the x direction (east-west) would give you:

-m_B*v_B=m_total*v_xtotal (note east taken to be positive x)
so you end up with
v_xtotal=-m_B*v_B/m_total=-119.4*50/395.9=-15.08m/s (negative means moving west)

Now use conservation of momentum in the y direction (north-south)

-m_A*v_A=m_total*v_ytotal (note north taken to be positive y)
so you end up with
v_ytotal=-m_A*v_A/m_total=-276.5*41/395.9=-28.6m/s (negative means moving south)

So now to get the direction of motion, just use the components of the overall velocity.

tan(theta)=y/x
theta=arctan(y/x)=arctan(-28.6/-15.08)=62.2deg (this is the angle with the x-axis)

So the direction will be 62.2deg south of west.

Answer 2

South West.

Answer 3

Southeast on a heading of 152.2 degrees.

OPPS!! Read the car A direction wrong. Answer should be southwest on a heading of 207.77 degrees.
Sorry

Answer 4

...South West....

Answer 5

ya right