91Ó°ÊÓ

The radius of the earth is $6400\text{km}$.

The plane must cover the total distance of the equator of earth in $24\text{h}$, in order to have zero relative distance of the passenger with the sun.

The speed of the plane is,

$v=\frac{d}{t}\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}\mathrm{....}\left(\text{l}\right)$

Here, v is the speed of the plane, d is the distance need to cover by the plane, $t$and is the period of time.

The total distance in the equator of the earth is,

$d=2\mathrm{Ï€}r$

Here, r is the radius of the earth.

$d=2\mathrm{Ï€}(6400\text{km})=40212.3\text{km}$

Substitute $40212.3\text{km}$for $d$and $24\text{h}$for $t$in the equation (I) to find $v$.

$v=\frac{40212.3\text{km}}{24\text{h}}=1675.5\text{km}/\text{h}$

Therefore, the speed of the plane in $\text{km}/\text{h}$must be $1675.5\text{km}/\text{h}$so that the passengers in the plane are still relative to the sun.

The radius of the earth is $6400\text{km}$.

From the solution of the part (a), the speed of the plane in $\text{km}/\text{h}$is $1675.5\text{km}/\text{h}$.

The speed of the plane from $\text{km}/\text{h}$to $\text{mph}$is,

$v=(x\text{km}/\text{h})\left(\frac{0.621371\text{miles}}{1\text{km}}\right)$-$v$is the speed of the plane in mph.

- $x$is the speed of the plane in $\text{km}/\text{h}$.

Substitute $1675.5\text{km}/\text{h}$for $x$in the above equation to find $v$.

$v=(1675.5\text{km}/\text{h})\left(\frac{0.621371\text{miles}}{1\text{km}}\right)=1041.1\text{mph}$Thus, the speed of the plane in mph is $1041.1\text{mph}$.

Therefore, the speed of the plane must be $1041.1\text{mph}$so that the passengers in the plane are still relative to the sun.

The radius of the earth is$6400\text{km}$.

Since the earth is rotating in the direction of west to east, so in order to maintain the sun at the constant sky the plane must be travel in the opposite direction of rotation of earth. Thus, the plane must flying in the direction ofeast to west.

Therefore, the plane must flying in the direction opposite of the direction of rotation of the earth, which is from east to west..