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Chapter 5: Q69P (page 1155)

You are in your car driving on a highway at 25m/swhen you glance in the passenger-side mirror (a convex mirror with radius of curvature 150 cm) and notice a truck approaching. If the image of the truck is approaching the vertex of the mirror at a speed of 1.9 m/swhen the truck is 2.0 m/sfrom the mirror, what is the speed of the truck relative to the highway?

Short Answer

Expert verified

The speed of the truck relative to the highway is 50.5444m/s.

Step by step solution

01

Determine the speed of the truck relative to the highway

The speed of the truck relative to the mirror is

Use the object-image relationship

Substitute the given values

Take a derivative of the object-image relationship

Substitute the values in the equation

Now, the truck velocity with respect to the ground equals truck velocity with respect to mirror plus mirror velocity with respect to ground

Therefore, the speed of the truck relative to the highway is 50.5444m/s.

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