Two cars are traveling on a single lane road in the same direction on a foggy da

Question

Two cars are traveling on a single lane road in the same direction on a foggy day. the car in front is blue, has a mass 1000 kg and has a velocity 40km/h. The car behind is red, has a mass of 2000 kg and is traveling with velocity 80 km/h. Assume the cars are moving in the positive x direction.

A) What is the velocity of the Centre of mass?

when the driver in the red sees the car in front, she immediately starts to brake, but is unable to avoid a collision. the red car his the blue car exactly when they reach an ice patch and neither car can brake. the blue car is observed to continue moving with velocity of 50 km/h and the car behind also continues to move in the same direction with velocity 47km/h.

B) what was the velocity of the red car (after brakes) when the two cars collided?

C)was the collision elastic or inelastic, explain .

D) magnitude of impulse on blue car due to collision?

Explanation / Answer

A)   velocity of the Centre of mass = (1000 * 40 + 2000 * 80)/3000

                                                        = 66.67 km/hr

B)   Applying conservation of momentum

=>    1000 * 40 + 2000 * v   = 1000 * 50 + 2000 * 47

=>   v   =   52 km/hr             ---------------------------> the velocity of the red car (after brakes)

C)       Relative velocity after collision =    3 km/hr

         Relative velocity before collision = 12 km/hr

=>    collision is inelastic   .

D)     magnitude of impulse on blue car due to collision = 1000 * (50 - 40)

                                                                                        = 10000 kg.m/sec

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