*18.  A stone held just beneath the surface of a swimming pool is released and sinks to the bottom at a constant speed of 0.48 m/s. What is the apparent speed of the stone, as viewed from directly above by an observer who is in air?

 

Since the speed is constant we know the relationship between speed, distance and time is given by

 

However, from above the stone falls an apparent distance d’ but it falls in the same time so it must be falling with a different speed, v’.  So combine these two relations assuming the time is the same and we have

 

Solve for apparent speed v’

 

Now recall that apparent depth is the virtual image  and we had the relationship

 

 

Now here we have the following relations

 

and

Also

And

So solving for d’/d

 

 

 

 

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This page last updated on July 1, 2018