Question

A migrating salmon heads in the direction N 45° E, swimming at 5 mi/h relative to the water. The prevailing ocean currents flow due east at 2 mi/h. Find the true velocity of the fish as a vector. (Assume that the i vector points east, and the j vector points north.)

Answer 1

Answer:

Explanation:

velocity of salmon with respect to water, v(s,w) = 5 mi/h at N 45° E

velocity of water with respect to ground, v(w,g) = 2 mi/h due east

Let the true velocity of salmon is velocity of salmon with respect to water is v(s,g)

First write the velocities in vector from

$\overrightarrow{v}_{s,w}=5(Cos 45\widehat{i}+Sin 45\widehat{j})=3.54\widehat{i}+3.54\widehat{j}$

$\overrightarrow{v}_{w,g}=2\widehat{i}$

Using the formula of relative speed,

$\overrightarrow{v}_{s,w}=\overrightarrow{v}_{s,g}-\overrightarrow{v}_{w,g}$

$3.54\widehat{i}+3.54\widehat{j}=\overrightarrow{v}_{s,g}-2\widehat{i}$

$\overrightarrow{v}_{s,g}=5.54\widehat{i}+3.54\widehat{j}$

This i the true velocity of salmon.