Air Navigation

Section 6.3

This question ends of Section 6.3. We move on to Section 6.4 aka Vectors & Dot Products. Can you do this one for me? I need parts (a - e). Thank you for your help.

 

A commercial jet travels from Miami to Seattle. The jet's velocity with respect to the air is 580 miles per hour, and its bearing is 332° . The jet encounters a wind with a velocity of 60 miles per hour from the southwest.
(a) Draw a diagram that gives a visual representation of the problem.


(b) Write the velocity of the wind as a vector in component form.

we can find velociti this way:

r^2=580^2+60^2-2(580)(60)cos(107)

r^2=340000-69600*cos(107)
r^2=340000-69600*(-0.292372)
r^2=360349.07
r=600.3mph

as a vector in component form, find vector ||Vw||
Magnitude [(cos θ)i + (sin θ)j] = (60cos 107°)i + (60sin 107°)j
||Vw||= (-17.54i + 57.38j)


(c) Write the velocity of the jet relative to the air in component form.

Magnitude [(cos θ)i + (sin θ)j] = (580cos (107°)i + (580sin (107°))j
||Vj||= (-169.58i +554.67j) miles per hour

(d) What is the speed of the jet with respect to the ground?
Suppose two bodies jet and wind are moving with velocity Vj and Vw respectively. These velocities are with respect to the ground (or a stationary observer).

the speed of the jet with respect to the ground: find vector u=Vj+Vw

u =(-272.3i + 525.7j)+(-28.17i + 52.98j)
u=(-300.47i + 578.68j)


(e) What is the true direction of the jet?

θ=tan(578.68/-300.47)=154.5°

 

1. Can you redraw the diagram? Such a tough question for a precalculus textbook.

 

simplest one

 

Ok. Much better.