A 1435 kg car traveling east with a speed of 28.0 m/s collides at an intersectio

Question

A 1435 kg car traveling east with a speed of 28.0 m/s collides at an intersection with a 2315 kg van traveling north at a speed of 22.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision.


The eastbound car is driven by an off-duty police officer, who knows her speed was exactly 30.0 m/s. From studying the angle (and the mass of the two vehicles), she concluded that the van was over the speed limit of 90 km/h driving on that secondary road. Of course, the van also failed to stop before entering the main road. If the van were not speeding, what should be the maximum angle for (in degrees) in this accident?

Explanation / Answer

Mass of the car m1 = 1435 Kg

Mass of the van m2 = 2315 Kg

Initial speed car u1 = 28 i m/s

Initial speed of van u2 = 22 j m/s

Let v be the common speed of the two vehicles after the collision.

According to law of conservation of momentum

                            m1 u1 + m2 u2 = (m1 + m2)v

                         40180 i + 50930 j = 3750 v

Final speed v = 10.714 i + 13.581 j

Magnitude : 17.298 m/s

Direction :   = Tan^-1[13.581/10.714] = 51.73 degrees north of east.                       

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