Calculating the Speed of a Plane for a Stationary Sun at 26.3° Latitude

[Tina20]

Homework Statement

How fast must a plane fly at a latitude of 26.3° so that the sun stands still relative to the passengers?

Homework Equations

I have no idea how I can solve this question. I would like to draw a free-body diagram, but I don't know how to do that either. If I could at least draw a diagram, it would help me to think through this question.

The Attempt at a Solution

I believe that the plane is 26.3 degrees above the equator, flying around the earth. So it is a circular motion question.

I don't have an acceleration, now do I have a period, but I think that the period might be one rotation around the earth, so 24 hours is one period? Also, the radius of the Earth is 6.37e6 m. angular velocity = speed/radius and angular velocity = 2pi/period

 

[willem2]

You indeed have a period of 24 hours.

The radius of the circle at a latitude of 26.3 degress is the distance from the Earth's axis to any point of this circle.
draw a picture of a crosssection through the Earth along the Earth's axis.

 

[Tina20]

Thank you! I drew the free body diagram, found the radius using 6.37x10^6 cos 26.3 deg. and then substituted the radius and the period (T) --> (24hours = 86400 sec) into v= 2pir/T and got the answer :)

 

[ghostanime2001]

Why do u need to know the freebody diagram?