Determining the speed

**jashansinghal** · April 27th 2010, 01:17 AM

A light house facing north sends out a fan shaped beam of light extending from north east to north west. An observer on a steamer , sailing due west ,first sees the light when he is 5 km away from the lighthouse and continues to see it for $30\sqrt2$ minutes.What is the speed of the steamer?

**Archie Meade** · April 27th 2010, 02:53 AM

Originally Posted by jashansinghal

A light house facing north sends out a fan shaped beam of light extending from north east to north west. An observer on a steamer , sailing due west ,first sees the light when he is 5 km away from the lighthouse and continues to see it for $30\sqrt2$ minutes.What is the speed of the steamer?

Hi jashansinghal,

In crossing the fan of light, the steamer will have travelled

$\sqrt{5^2+5^2}=\sqrt{25+25}=\sqrt{50}\ km$

using Pythagoras' theorem.

$t=30\sqrt{2}\ minutes=\frac{30\sqrt{2}}{60}\ hours=\frac{\sqrt{2}}{2}\ hours$

$av.\ speed=\frac{distance}{time}=\frac{\sqrt{50}}{\left (\frac{\sqrt{2}}{2}\right)}$

$=\frac{2\sqrt{50}}{\sqrt{2}}=\frac{\sqrt{50}\sqrt{ 2}\sqrt{2}}{\sqrt{2}}$

$=\sqrt{50}\sqrt{2}=\sqrt{2(50)}=\sqrt{100}=$ 10 km per hour

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