You are driving North through an intersection in a 55 mi/hr speed zone, when the

Question

You are driving North through an intersection in a 55 mi/hr speed zone, when the local Chief of Police, who is driving his new Cadillac and approaching the intersection from the West, hits you broadside. The two cars stick together and skid a distance 28.4 m with locked wheels at an angle of 63.1° to the East of North. The mass of your car is 1557.0 kg while the Cadillac has a mass 2087.0 kg. The coefficent of sliding friction is 0.90. The Chief of Police is angry 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 prior to the collision.

Compute your speed immediately prior to the collision as evidence for or against the speeding ticket.

Explanation / Answer

after collision

distance = s = 28.4 m

work done by friction = Wf = uk*(m1+m2)*g*s

from work energy theorem

work done = change in KE

uk*(m1+m2)*g*s = 0.5*(m1+m2)*v^2

0.9*9.8*28.4 = 0.5*v^2

v = 22.4 m/s

after collision velocity v = 22.4*sin63.1i + 22.4*cos63.1j

v = 20 i + 10.1 j

m1 = 1557 kg      v1 = 55mi/h j = 24.6 j m/s

m2 = 2087 kg        v2 = v2i

from momentum conservation

momentum before collision = momentum after collision

m1*v1 + m2*v2 = (m1+m2)*v

(1557*24.6j) + (2087*v2i) = (1557+2087)*(20 i + 10.1 j)

comparing i

2087*v2 = (1557+2087)*20

v2 = 35 m/s

speed of Chief of police > speed of you

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.