Problem:  A car with mass mc = 1134 kg is traveling west through an intersection at a magnitude of velocity of vc = 9.5 m/s when a truck of mass mt 1752 kg traveling south at vt = 8.8 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction of μk = 0.5.A) Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and jB) How far, in meters, will the vehicles slide after the collision?

FREE Expert Solution

Law of conservation of momentum:

P0=Pfmcvc(-i^)+mtvt(-j^)=(mc+mt)vct

We'll also use the kinematic equation;

vf2=v02+2ax

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Problem Details

 A car with mass mc = 1134 kg is traveling west through an intersection at a magnitude of velocity of vc = 9.5 m/s when a truck of mass mt 1752 kg traveling south at vt = 8.8 m/s fails to yield and collides with the car. The vehicles become stuck together and slide on the asphalt, which has a coefficient of friction of μk = 0.5.

A) Write an expression for the velocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j

B) How far, in meters, will the vehicles slide after the collision?