Q69P - University Physics with Modern Physics

Question

You are in your car driving on a highway at 25m/s when 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/s when the truck is 2.0 m/s from the mirror, what is the speed of the truck relative to the highway?

Step-by-Step Solution

Answer

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

Step 1: 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.