Question

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1400 kg , is going from north to south at 12.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 65.0 ∘ south of east from the point of impact. Part A How fast were the enmeshed cars moving just after the collision? Part B How fast was car A going just before the collision?

Answer 1

This is an inelastic collision.

Here we can use conservation of momentum

In x - direction

mAvAi + mBvBi = (mA + mB)v_x

2000 * vAi + 0 = ( 2000 + 1400) vcos65

In y - direction

0 - 1400 * 12 = ( 2000 + 1400)( - v sin 65)

- 16800 = -3400 * v * sin 65

v = 5.45 m/s ( this is the combined velocity after collision)

----------------------------

use this to find initial velocity of car A

2000 * vAi + 0 = ( 2000 + 1400) vcos65

2000 * vAi + 0 = ( 2000 + 1400) * 5.45* cos65

vA = 3.92 m/s