Two automobiles of equal mass approach an intersection. One vehicle is traveling

Question

Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 12.5 m/s toward the east and the other is traveling north with speed v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 57.5° north of east. Determine the initial speed v2i of the northward-moving vehicle.
________ m/s

The speed limit for both roads is 35 mi/h and the driver of the northward-moving vehicle claims he was within the speed limit when the collision occurred. Is he telling the truth?

Yes or No     

Explanation / Answer

We use conservation of momentum for thesystem of two vehicles for both northward and eastward components.

For the eastward direction:

M(12.5) = 2MVf cos(57.5º)

For the northwarddirection:

Mv2i= 2MVf*sin(57.5°)

Divide the northward equation by the eastward equation to find:

v2i = (12.5m/s)tan(57.5º)= 19.62 m/s = 43.89 mi/hr

Thus, the driver of the north bound car was untruthful.

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