Question

A jet airliner moving initially at 3.10 multiply.gif 102 mi/h due east enters a region where the wind is blowing at 1.00 multiply.gif 102 mi/h in a direction 24.5° north of east. (Let the x-direction be eastward and the y-direction be northward.)

(a) Find the components of the velocity of the jet airliner relative to the air, v with arrowJA.

vJA,x = mi/h
vJA,y = mi/h
(b) Find the components of the velocity of the air relative to Earth, v with arrowAE.

Answer 1

Answer:

(a). The components of the velocity of the jet airliner relative to the air is

$v_{JA_{x}}=3.10\times10^{2}\ mi/h$

$v_{JA_{y}}=0$

(b). The components of the velocity of the air relative to earth is

$v_{AE_{x}}=0.90\times10^{2}\ mi/h$

$v_{AE_{y}}=0.41\times10^{2}\ mi/h$

Explanation:

Given that,

Initial speed of jet $v_{i}=3.10\times10^{2}\ mi/h$

Speed of wind = 1.00\times10^{2}\ mi/h[/tex]

Angle = 24.5°

(a). We need to calculate the components of the velocity of the jet airliner relative to the air,

Using formula of velocity

The components of the velocity

$v_{JA_{x}}=3.10\times10^{2}\ mi/h$

$v_{JA_{y}}=0$

(b).  We need to calculate the components of the velocity of the air relative to earth,

Using formula of the components of the velocity

For x-axis,

$v_{AE_{x}}=v_{w}\cos\theta$

Put the value into the formula

$v_{AE_{x}}=1.00\times10^{2}\cos24.5$

$v_{AE_{x}}=0.90\times10^{2}\ mi/h$

For y axis,

$v_{AE_{y}}=1.00\times10^{2}\sin24.5$

$v_{AE_{y}}=0.41\times10^{2}\ mi/h$

Hence, (a). The components of the velocity of the jet airliner relative to the air is

$v_{JA_{x}}=3.10\times10^{2}\ mi/h$

$v_{JA_{y}}=0$

(b). The components of the velocity of the air relative to earth is

$v_{AE_{x}}=0.90\times10^{2}\ mi/h$

$v_{AE_{y}}=0.41\times10^{2}\ mi/h$