Question

A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is blowing due north with a speed of 30 mi/h. (Assume that the i vector points east, and the j vector points north.)
a. Express the velocity of the wind as a vector in component form.
b. Express the velocity of the jet relative to the air as a vector in component form.
c. Find the true velocity of the jet as a vector.
d. Find the true speed of the jet. (Round your answer to the nearest integer.)
e. Find the direction of the jet.

Answer 1

Explanation:

a. The velocity of the wind as a vector in component form will be represented as v vector:

    $v=30j$

b.The velocity of the jet relative to the air as a vector in component form will be represented as u vector

    $u=475i$

c. The true velocity of the jet as a vector will be represented as w:

  $w=u+v$

  $w=475i+30j$

d.  The true speed of the jet will be calculated as:

    $IwI=\sqrt{(475)^2+(30)^2}$

    $IwI=\sqrt{225625+900}$

    $IwI=\sqrt{226525}$

    $IwI=476 mi/h$

e. The direction of the jet will be:

$tita=tan^{-1}\frac{30}{475}$

$tita=tan^{-1}(0.0632)$

$tita=3.62degrees,or,N86.38degreesS$