Car Accident?

Question

Car Accident
You are the juror of a case involving a drunken driver whose 1049.0 kg sports car ran into a stationary 2092.0 kg station wagon stopped at a red traffic light. The cars stuck together and slid with locked wheels for 10.0 m before coming to rest. The coefficient of sliding friction on the dry road was 0.9. Estimate the speed of the sports car when it hit the station wagon.

I only have one try left on this problem..Please help

Answer 1

a = μ g = 0.9 x 9.8 = 8.82
v^2 = 2a S = 2 x 8.82 x 10 = 176.4
v = 13.28 m/s.
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Using Conservation of momentum
m1 u1 = [m1 +m2] v
u1 = 3141 x 13.28 / 1049 = 39 .76 m /s

Answer 2

THe work done by friction is:

Wf = f*x =u*(mc+mw)*g*x where u = coefficient of friction, mc = mass of car, mw = mass of station wagon, g = 9.8 ms/^2

Plugging in numbers

Wf = 0.9*(1049+2092)*9.8*10 = 277036.2 J

Assume that the cars don't use up energy in sticking together. Then the work done is equal to the kinetic energy of the sports cars;

1/2mc*v^2 = 227036.2 J -->v = sqrt(2*227036.2/1049) = 23 m/s