contestada

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.)

Respuesta :

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

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

[tex]\overrightarrow{v}_{w,g}=2\widehat{i}[/tex]

Using the formula of relative speed,

[tex]\overrightarrow{v}_{s,w}=\overrightarrow{v}_{s,g}-\overrightarrow{v}_{w,g}[/tex]

[tex]3.54\widehat{i}+3.54\widehat{j}=\overrightarrow{v}_{s,g}-2\widehat{i}[/tex]

[tex]\overrightarrow{v}_{s,g}=5.54\widehat{i}+3.54\widehat{j}[/tex]

This i the true velocity of salmon.

onyebuchinnaji

The true velocity of the fish as a vector is [tex]5.54i \ + \ 3.54j[/tex].

The given parameters;

  • velocity of the salmon relative to the water, = 5 mi/h
  • direction of the velocity, θ = 45⁰
  • ocean currents, = 2 mi/h

The true velocity of the fish as a vector is calculated as follows;

[tex]v_f = v\ cos(\theta)i \ + \ v\ sin(\theta)j \ + \ 2i\\\\v_f = 5cos(45) i \ + 5sin(45)j \ + \ 2i\\\\v_f = 3.54i \ + \ 3.54j \ + 2i\\\\v_f = 5.54i \ + \ 3.54 j[/tex]

Thus, the true velocity of the fish as a vector is [tex]5.54i \ + \ 3.54j[/tex].

Learn more here:https://brainly.com/question/4945130

Otras preguntas