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\sqrt2minutes.What is the speed of the steamer?

Asked by prakharagarwal1405 | 7th May, 2014, 05:56: PM

Expert Answer:

L e t space x space b e space t h e space s p e e d space o f space t h e space s t e a m e r. T h e space d i s tan c e space o f space t h e space o b s e r v e r space o n space a space s t e a m e r space f r o m space t h e space l i g h t space h o u s e space i s space 5 space k m. S i n c e space t h e space o b s e r v e r space c o n t i n u e s space t o space s e e space i t space w h e n space t r a v e l l i n g space f r o m space e a s t space t o space w e s t comma space u sin g space P y t h a g o r a s space T h e o r e m comma space t h e space d i s tan c e space c o v e r e d space b y space t h e space o b s e r v e r space i s space square root of 5 squared plus 5 squared end root equals square root of 50 k m. G i v e n space t h a t space t equals 30 square root of 2 space m i n u t e s equals fraction numerator 30 square root of 2 over denominator 60 end fraction h o u r s equals fraction numerator square root of 2 over denominator 2 end fraction space h o u r s S p e e d equals fraction numerator D i s tan c e over denominator T i m e end fraction equals fraction numerator square root of 50 over denominator fraction numerator square root of 2 over denominator 2 end fraction end fraction equals fraction numerator 2 square root of 50 over denominator square root of 2 end fraction equals square root of 2 square root of 50 equals square root of 100 space k m space p e r space h o u r equals 10 space k m space p e r space h o u r
 
Thus, x=10 km per hour

Answered by Vimala Ramamurthy | 8th May, 2014, 11:24: AM

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