Question

A pilot heads his jet due east. The jet has a speed of 425 mi/h relative to the air. The wind is blowing due north with a speed of 35 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 and direction of the jet.

Answer 1

Answer:

(a)Velocity of wind = 35 j

(b)Velocity of jet relative to air = 425 i

(c)True velocity of jet = 425 i + 35 j

(d)True speed of jet = $\sqrt{425^{2}+35^{2}}$ = 426.88 mi/h

    Direction of jet is, ∅ = $tan^{-1} \frac{40}{425}$ = 5.38°

Explanation:

We can represent east direction by i and north direction by j.

The jet has a relative speed of 425 mi/h relative to the air.

The wind is blowing due north with a speed of 35 mi/h = 35 j

425 mi/h is the relative speed with respect to wind that is

Velocity of jet wrt wind= $V_{jw}$ = $V_{j}-V_{w}$

                               425 i = $V_{j}$ - 35 j

$V_{j}$ = 425 i + 35 j

(a)Velocity of wind = 35 j

(b)Velocity of jet relative to air = 425 i

(c)True velocity of jet = 425 i + 35 j

(d)True speed of jet = $\sqrt{425^{2}+35^{2}}$ = 426.88 mi/h

    Direction of jet is,

     ∅ = $tan^{-1} \frac{40}{425}$ = 5.38°