Question

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.)

Answer 1

Answer:

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

Step-by-step explanation:

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

$\overrightarrow{V_{R,G}}=4(\widehat{-j})$

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

$\overrightarrow{V_{S,R}}=2(\widehat{i})$

According to the formula of relative velocity

$\overrightarrow{V_{S,R}}=\overrightarrow{V_{S,G}}-\overrightarrow{V_{R,G}}$

$2\widehat{i}=\overrightarrow{V_{S,G}}+4\widehat{j}$

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

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