A car with a mass of 1,400 kg and a speed o 15 m/s heading north approaches an i

Question

A car with a mass of 1,400 kg and a speed o 15 m/s heading north approaches an intersection. At the same time, a minivan with a mass of 1,800 kg and speed of 20 m/s heading east is also approaching the intersection. The car and the minivan collide and stick together. What is the velocity of the wrecked vehicles just after the collision? Ignore friction between the tires and the surface of the road. (Enter the magnitude in m/s and the direction in degrees counterclockwise from due east.) magnitude direction m/s o counterclockwise from due east

Explanation / Answer

Using momentum conservation

In x-direction

Pix = Pfx

m1V1xi + m2*V2xi = (m1 + m2)*Vxf

V1xi = 0

Vxf = Vf*cos A = m2*V2xi/(m1 + m2)

m1 +m2 = 3200 kg

Vf*cos A = 1800*20/3200 = 11.25 m/sec

Similarly

In y-direction

Vyf = Vf*sin A = m1*V1yi/(m1 + m2)

Vf*sin A = 1400*15/3200 = 6.56 m/sec

Vxf = 11.25 m/sec

Vyf = 6.56 m/sec

Vf = sqrt (Vxf^2 + Vyf^2)

Vf = sqrt (11.25^2 + 6.56^2)

Vf = 13.02 m/sec

Angle theta will be

A = arctan (Vyf/Vxf)

A = arctan (6.56/11.25) = 30.25 deg

Vf = 13.02 m/sec at 30.25 deg CCW from east

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