A car with mass Mc=1418 kg is traveling west through an intersection at a magnit

Question

A car with mass Mc=1418 kg is traveling west through an intersection at a magnitude of the velocity of Vc=8.5 m/s when a truck of mass Mt=1577 kg traveling south at Vt=10.2 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 uk=0.5. 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. How far, in meters, will the vehicles slide after the collision?

Explanation / Answer

Applying momentum conservation for the collision,

Mc Vc (-i) + Mt Vt (-j) = (Mc + Mt) v

v = - Mc Vc / (Mc + Mt) i - Mt Vt / (Mc + Mt) j

----Expression for velocity .

Computing values,

v = -4.02i - 5.37j

Speed = sqrt(4.02^2 + 5.37^2) = 6.71 m/s ....Ans

a = - uk g = - 4.9 m/s^2

Applying vf^2 - v0^2 = 2 a d

0^2 - 6.71^2 = 2(-4.9)d

d = 4.59 m .......Ans

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