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 11.1 m/s toward the east, and the other is traveling north with velocity v2i. Neither driver sees the other. The vehicles collide in the intersection and stick together, leaving parallel skid marks at an angle of 60.4° north of east. The speed limit for both roads is 35 mi/h, and the driver of the northward-moving vehicle claims he was within the limit when the collision occurred. Is he telling the truth?

What was the initial speed of the northward-moving vehicle?

____mi/h

Explanation / Answer

using momentum conservation for collision,

m x 11.1i + m x v2 j = 2m v (cos60.4i + sin60.4j )

along i

11.1m = 2mvcos60.4

v = 11.24 m/s

along j

mv2 = 2m x 11.24 x sin60.4

v2 = 19.54 m/s

so initial speed was 19.54 m = 19.54 x 1/1609 mi x 3600 hr

= 43.72 mi /h

so , he was lying.

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