How fast must a plane fly along the earth’s equator so

Problem 40GP Chapter 6

Physics: Principles with Applications | 6th Edition

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Physics: Principles with Applications | 6th Edition

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Problem 40GP

How fast must a plane fly along the earth’s equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both km/h and mph. The radius of the earth is 6400 km.

Step-by-Step Solution:

Solution Step 1 of 6 In order to see the sun as static on the equator of the earth in a plane. The plane must have the speed same as that of the earth. Which means the plane should also complete one full revolution around the earth in the same time as earth completes one rotation about its axis of rotation; one complete revolution or rotation in 24 hours. Step 2 of 6 Also as the earth performs the rotation about the axis, from west to east. The plane must perform revolution around the earth on the equator from east to west with the same speed as that of the earth rotation speed.So that sun appears static, As shown in the figure below Step 3 of 6 Angular displacement (d) When a particle moves along the circumference of the circle, the radius drawn from the center of the particle position rotates through a certain angle. The angle through which the radius turns is called angular displacement (d). The SI unit of angular displacement is radian (rad). Angular speed() The rate at which the body rotates or angular position of the body changes is called Angular speed. It is given by, = Angular displacement / time taken= dt radians/Sec Where, is the angular speed,d is the angular displacement and dt is the time taken.

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