**Part (a)**

From the conservation of momentum:

m_{c}v_{c} + m_{t}v_{t} = (m_{c} + m_{t})v_{f}

v_{f} = (m_{c}v_{c} + m_{t}v_{t})/(m_{c} + m_{t})

A car with mass m_{c} = 1353 kg is travelling west through an intersection at a magnitude of velocity of v_{c} = 6.5 m/s when a track of mass m_{t}= 1647 kg travelling south at v_{t} = 15 A 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 μ_{k} = 0.5.

Part (a) Write an expression for the veolocity of the system after the collision, in terms of the variables given in the problem statement and the unit vectors i and j.

Part(b) How far, in meters, will the vehicles slide after the collision?

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