A ship is travelling due east with a peed 4m+s relative to water which flows due north with a speed of 3m+s a south eastern wind flows with a speed of2^1+2 relative to ground then find velocity of wind relative to the ship in m/s. Answe-5

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$L e t p o s i t i v e X a x i s a l o n g e a s t a n d p o s i t i v e y a x i s a l o n g n o r t h V e l o c i t y o f s h i p w i t h r e s p e c t t o r i v e r : {\vec{V}}_{s h i p, r i v e r} = 4 \hat{i} m / s V e l o c i t y o f r i v e r w i t h r e s p e c t t o g r o u n d : {\vec{V}}_{r i v e r, g r o u n d} = 3 \hat{j} m / s V e l o c i t y o f s h i p w i t h r e s p e c t t o g r o u n d i s {\vec{V}}_{s h i p, g r o u n d} = {\vec{V}}_{s h i p, r i v e r} + {\vec{V}}_{r i v e r, g r o u n d} = (4 \hat{i} + 3 \hat{j}) V e l o c i t y o f w i n d w i t h r e s p e c t t o t h e g r o u n d a s s h o w n i n t h e f i g u r e w i t h i t s c o m p o n e n t i s {\vec{V}}_{w i n d, g r o u n d} = (\hat{i} - \hat{j}) m / s V e l o c i t y o f t h e w i n d w i t h r e s p e c t t o t h e s h i p i s {\vec{V}}_{w i n d' s h i p} = {\vec{V}}_{w i n d, g r o u n d} - {\vec{V}}_{s h i p, g r o u n d} {\vec{V}}_{w i n d' s h i p} = (\hat{i} - \hat{j}) - (4 \hat{i} + 3 \hat{j}) = - 3 \hat{i} - 4 \hat{j} m a g n i t u d e o f {\vec{V}}_{w i n d' s h i p} i s |{\vec{V}}_{w i n d' s h i p}| = \sqrt{3^{2} + 4^{2}} = 5 m / s R e g a r d s$

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