91影视

From the formula of relative velocity of any object,

If any object P is moving related to A and A is moving related to E, then the velocity of P related to E is,

$V_{P/E}=V_{P/A}+V_{A/E}$

For horizontal motion, localid="1659538616006">VP/Ah=-220Km/h

For vertical motion,$V_{P/A_v}=0Km/h$

For horizontal motion,

$V_{P/A_h}=-220Km/h$

For vertical motion,

$V_{P/A_v}=0Km/h$

The wind velocities for horizontal and vertical motion are respectively,

$$\begin{gathered} V_{P/E_h}=-\frac{120}{0.500}Km/h \\ {V}_{P/E_h}=-240Km/h\left(west\right) \\ {V}_{P/E_v}=-\frac{20}{0.500}Km/h \\ {V}_{P/E_v}=-40Km/h\left(south\right) \end{gathered}$$

With the given information the following figure can be drawn

From both the horizontal component of velocity that is $V_{P/A_h}=-220Km/h$and $V_{P/E_h}=-240Km/h\left(west\right)$

$$\begin{gathered} V_{P/E_h}=V_{P/A_h}+V_{A/E_h} \\ {V}_{P/E_h}=-240Km/h-(-220Km/h) \\ {V}_{P/E_h}=-20Km/h \end{gathered}$$

The vertical components of velocity $V_{P/A_V}=0Km/h$and $V_{P/E_V}=-40Km/h\left(south\right)$

localid="1659540728505" $$\begin{gathered} V_{P/E_V}=V_{P/A_V}+V_{A/E_V} \\ {V}_{A/E_V}=-40Km/h-(-0Km/h) \\ {V}_{A/E_V}=-40Km/h \end{gathered}$$

Now the velocity magnitude will be

localid="1659540477517" $$\begin{gathered} V_{A/E}=\sqrt{{\left(V_{A/E_V}\right)}^2+{\left(V_{A/E_h}\right)}^2} \\ {V}_{A/E}=\sqrt{{\left(-40Km/h\right)}^2+{\left(-20Km/h\right)}^2} \\ {V}_{A/E}=44.7Km/h \end{gathered}$$

The angle or direction will be,

$$\begin{gathered} \tan 蠒=\frac{-40Km/h}{-20Km/h} \\ 蠒=63.4掳 \end{gathered}$$

The $Magnitude{V}_{A/E}=44.7Km/h$and direction of wind velocity is $63.4掳$south of west .

According to vector rule,

$V_{P/E}=V_{P/A}+V_{A/E}$

$V_{P/A}and{V}_{A/E}$are $220Km/hand40Km/h\left(south\right)$

The vector diagram of will be and the direction will be at right angle as shown in figure

From the above figure,

$$\begin{gathered} \sin 蠒=\frac{V_{A/E}}{V_{P/E}} \\ \sin 蠒=\frac{40Km/h}{220Km/h} \\ 蠒=10.5掳 \end{gathered}$$

The course should be set by the pilot toward $10.5掳$snorth of west.