Question

A patient is placed in an elliptical tank that is 178 centimeters long and 102 centimeters wide to undergo sound wave lithotripsy treatment for kidney stones. Determine where the sound emitter and the stone should be positioned relative to the center of the tank

Answer 1

Complete Question

The  diagram for this question is shown on the first uploaded image

Answer:

The position of the emitter is  $E = + 72.9 \ cm\ from\ the\ center$

The position of the stone is   $S = - 72.9 \ cm\ from\ the\ center$

Step-by-step explanation:

From the question we are told that

   The  length is  l =  178 cm

    The  width is  w  =  102 cm  

Generally the position of the stone along the horizontal axis is mathematically evaluated as

         $h = \frac{178}{2}$

=>      $h = 89 \ cm$

Generally the position of the emitter along the vertical axis is mathematically evaluated as

         $k = \frac{102}{2}$

=>      $k = 51 \ cm$      

Generally the  resultant position of both stone and the emitter is

       $R = \pm \sqrt{h^ 2 - k^2}$

=>     $R = \pm \sqrt{89^ 2 - 51^2}$

=>     $R = \pm 72.9 \ cm$

Hence the position of the emitter is  $E = + 72.9 \ cm$

            the position of the stone is   $S = - 72.9 \ cm$