How fast must a jet fly to keep the sun directly overhead

[RPMACS]

A jet is traveling westward with the sun directly overhead. That is, the jet is on a line between the sun and the center of the earth. How fast must the jet fly in order to keep the sun directly overhead? Assume that the earth’s radius is 3960 miles, the altitude of the jet is low, and the earth rotates about its axis once in 24 hours.

Please help me with this problem.

 

[galactus]

I assume by 'the altitude of the jet is low' means its height is negligible compared to the earth's radius, so it can be otherwise ignored.

The Earth has a circumference of \(\displaystyle 2{\pi}3960=7920{\pi}\approx 24881 \;\ miles\)

That means it rotates \(\displaystyle \frac{24881}{24}=\approx 1037 \;\ mph\)

So, the jet will have to fly about 1037 mph.

Unless there is some Keplerian equation to use here.

 

[soroban]

Hello, RPMACS!

I thought this could be a trick question.

A jet is traveling westward with the sun directly overhead.
That is, the jet is on a line between the sun and the center of the earth.
How fast must the jet fly in order to keep the sun directly overhead?
Assume: the earth’s radius is 3960 miles, the altitude of the jet is low, and the earth rotates about its axis once in 24 hours.

I completely agreed with Galactus' solution
. . then had a thought (always a dangerous event).

There are some assumptions that we made:
. . The plane is circumnavigating at the Equator.
. . The Earth is "upright" relative to its ecliptic.

After making a number of sketches,
. . I found that these assumptions must be true
. . to satisfy the conditions of the problem.


Oh well, thought I'd share the jouney of ny wandering brain.

 

[RPMACS]

You guys are great. The problem makes sense when you put it on paper... I still have problems getting solutions started.

THANKS