# A jet is flying…

A jet is flying through a wind that is blowing with a speed of 95 mi/h in the direction N 35° E. The jet has a speed of 790 mi/h relative to the air, and the pilot heads the jet in the direction N 40° E (a) Express the velocity, u, of the wind as a vector in component form. (b) Express the velocity, v, of the jet relative to the air as a vector in component form. (c) Find the true velocity, w of the jet as a vector. (d) Find the true speed, | w |, and direction, θ, of the jet.

1. Let $V_jet$ be the absolute velocity of the jet (relative to the ground). Then as text says

$|w|= V_{jet} = V_{relative}+V_{air} = 790+95 =885 mph$

Let the SN direction be the y axis and WE direction be the x axis. Let j (on y axis) and i (on x axis) be the unity vectors on these axes.

a) $u = V_{air}*cos(35)*j + V_{air}*sin(35)*i = 95*cos(35)*j +95*sin(35)*i = 54.49*i + 77.82*j$

b) $V_r = V_{relative}*cos(40)*j +V_{relative}*sin(40)*i = 790*sin(40)*i +790*cos(40)*j =$ $=507.8*i+605.18*j$

c) $w = V_{jet}*cos(40)*j +V_{jet}*sin(40)*i = 885*sin(40)*i +885*cos(40)*j =568.87*i +677.95*j$

d) $|w| =885mph$

The direction $\theta$ relative to the x axis is $\theta = 90-40 =50 degree$