   Chapter 6, Problem 52P

Chapter
Section
Textbook Problem

Two automobiles of equal mass approach an intersection. One vehicle is traveling with velocity 13.0 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 55.0° 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?

To determine
Whether the driver of the north-ward moving vehicle is telling the truth or not.

Explanation

Given Info:

The velocity of the vehicle travelling to east direction is 13.0m/s .

The velocity of the vehicle travelling to north direction is v2i .

The parallel skid marks at an angle of 55.0° north of east.

The speed limit of both the roads is 35.0mi/h .

Consider the conservation of momentum in both the cases.

In the east-ward direction,

m(ve)=2mvfcosθ (I)

• m is the mass of the vehicle
• vf is the final velocity in the direction
• ve is the velocity of the vehicle in the east direction
• θ is the angle made by the skid

In the north-ward direction,

mv2i=2mvfsinθ (II)

Divide the equation (II) with (I),

mv2im(ve)=2mvfsinθ2mvfcosθ

Re-write the expression,

v2i=(ve)tanθ

Substitute 13

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