You are driving North through an intersection in a 55 m/hr zone, when the local
ID: 1552911 • Letter: Y
Question
You are driving North through an intersection in a 55 m/hr zone, when the local Chief of Police, who is driving his new Cadillac and approaching the speed intersection from the West, hits you broadside. The two cars stick together and skid a distance 32.8 m with locked wheels at an angle of 61.4 degree to the East of a North. The mass of your car is 1566.0 kg while the Cadillac has mass 1911.0 kg. The sliding friction is 0.80. The Chief of Police that you have damaged his new Cadillac and gives, you a ticket for speeding. The local judge is going to believe his Chief of Police rather than some out-of-town student. You realize that the knowledge you learned in your physics course is your only hope for acquittal. Compute the speed of the Chief of Police immediately the collision. Compute your speed immediately prior to the collision as evidence for or against the speeding ticket.Explanation / Answer
Let, final combined velocity = v2
KE immediately after collision,
KE = (1/2)*(ma + mb)*v2^2
Heat dissipated by friction after coming to rest after collision,
Q = u*N*d = u*(ma + mb)*g*d
From work energy theorem,
(1/2)*(ma + mb)*v2^2 = u*(ma + mb)*g*d
v2 = sqrt (2*u*d*g)
v2 = sqrt (2*0.8*32.8*9.8) = 22.67 m/s
By conservation of momentum,
mb*Vb = (ma+mb)*v2*sin(theta)
where Vb = speed of police prior to collision.
Vb = (ma+mb)*v2*sin(theta) / mb = (1566 + 1911)*22.67*sin(61.4) / 1911
Vb = 36.22 m/s
ma*Va = (ma+mb)*v2*cos(theta)
where Va = speed of your car.
Va = (1566 + 1911)*22.67*coa(61.4) / 1566
Va = 19.75 m/s
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