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A river flows due south at 4 mi/h. A swimmer attempting to cross the river heads due east swimming at 2 mi/h relative to the water. Find the true velocity of the swimmer as a vector. (Assume that the i vector points east, and the j vector points north.)

Respuesta :

Answer:

[tex]\overrightarrow{V_{S,G}}=2\widehat{i}-4\widehat{j} mi/h[/tex]

Step-by-step explanation:

velocity of river with respect to ground = 4 mi/h south

[tex]\overrightarrow{V_{R,G}}=4(\widehat{-j})[/tex]

Velocity of swimmer with respect to river = 2 mi/h east

[tex]\overrightarrow{V_{S,R}}=2(\widehat{i})[/tex]

According to the formula of relative velocity

[tex]\overrightarrow{V_{S,R}}=\overrightarrow{V_{S,G}}-\overrightarrow{V_{R,G}}[/tex]

[tex]2\widehat{i}=\overrightarrow{V_{S,G}}+4\widehat{j}[/tex]

Where, V(S,G) be the velocity of swimmer with respect to ground, it is true velocity of swimmer.  

[tex]\overrightarrow{V_{S,G}}=2\widehat{i}-4\widehat{j} mi/h[/tex]

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