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 October 19th, 2015, 02:21 PM #1 Senior Member   Joined: Jan 2015 From: London Posts: 108 Thanks: 2 Proportionality Hard Worded Question The pressure on a diver under water is directly proportional to the square of her depth below the surface of the water. The diver has reached a depth of 10 metres. How much further must she descend for the pressure to double?
October 19th, 2015, 03:07 PM   #2
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Quote:
 The pressure on a diver under water is directly proportional to the square of her depth below the surface of the water.
$P = k \cdot d^2$, where $k$ is the constant of proportionality

$2P = 2k \cdot d^2$

$2P = k \cdot 2d^2$

$2P = k \cdot (\sqrt{2} \cdot d)^2$

 October 20th, 2015, 07:55 AM #3 Senior Member   Joined: Jan 2015 From: London Posts: 108 Thanks: 2 Could you please expand on your answer so that we actually know how much further she has gone before the pressure doubles
October 20th, 2015, 02:16 PM   #4
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Quote:
 Originally Posted by jamesbrown Could you please expand on your answer so that we actually know how much further she has gone before the pressure doubles
final depth - initial depth ...

$\sqrt{2} \cdot d - d = d(\sqrt{2}-1)$

now substitute the given value for the initial depth into the expression.

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