Two cars collide at an intersection. Car A , with a mass of 1900 kg , is going f

Question

Two cars collide at an intersection. Car A , with a mass of 1900 kg , is going from west to east, while car B , of mass 1400 kg , is going from north to south at 17.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. 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.

How fast were the enmeshed cars moving just after the collision?

How fast was car A going just before the collision?

Explanation / Answer

using the conservstion of momentum

( 1900 + 1400 ) V = 1900 X VA i + 1400 VB ( - j )

33 V = 19 VA i - 14 VB j

V = 19 VA i / 33 - 14 X 17 j / 33

V = 19 VA i / 33 - 238 j / 33

tan 65 = ( 238 / 33 ) / ( 19 VA / 33 )

2.144 X 0.5757 X VA = 7.2121

VA = 5.84 m/sec

V = 19 VA i / 33 - 238 j / 33

V = 19 X 5.84 i / 33 - 238 j / 33

V = 3.36 i - 7.21 j

the speed were the enmeshed cars moving just after the collision

V = ( 3.362 + 7.212 )1/2

V = 7.95 m/sec

the velocity of A before collision is 7.21 m/sec

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