Your 2000 kg car was stopped in traffic in the middle of an intersection when th

Question

Your 2000 kg car was stopped in traffic in the middle of an intersection when the light turned red. A truck of unknown mass mt traveling along the cross road did not see your car and sideswiped it. Causing both vehicles to slide across the road leaving the skid marks shown in the diagram. The skid marks from the truck are 20 m long and are at an (average) angle of 10 degrees relative to the direction the truck had been driving. The skid marks from the car are 10m long at a 45 degree angle to the direction the truck had been driving. For rubber on concrete, s=1.0, and k=0.8. What was the velocity of the truck before the collision?

Explanation / Answer

Assuming that the truck applied brakes after collision
let its initial velocity be u

then initial momentum of the system = mt*u ( where mass of truck is unknown)

momentum of the system after collision, in the same direction
2000*u'*cos(45) + mt*v'*cos(10) [ where, u' is velocity of the car aftrer collision, and the v' is the velocity of the truck after collision]
now from the given data and equations of kinematics
2*(0.8*9.81)*10 = u'^2
and 2*(0.8*9.81)*20 = v'^2
u' = 12.606 m/s
v' = 17.718 m/s

so from conservation of momentum
mt*u = 2000* 12.606*cos(45) + mt*17.718*cos(10)
and
2000* 12.606*sin(45) = mt*17.718*sin(10)
so, mt = 5794.385 kg

and u = 20.526 m/s

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

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