Question

At the equator, the radius of the Earth is approximately 6370 km. A plane flies at a very low altitude at a constant speed of v = 219 m/s. Upon landing, the jet can produce an average deceleration of a=17 m/s^2. How long will it take the plane to circle the Earth at the equator?

Answer 1

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. For this purpose we will define the speed as the distance traveled in a given period of time. Here the distance is equivalent to the orbit traveled around the earth, that is, a circle. Approaching the height of the aircraft with the radius of the earth, we will have the following data,

$R= 6370*10^3 m$

$v = 219m/s$

$a = 17m/s^2$

The circumference of the earth would be

$\phi = 2\pi R$

Velocity is defined as,

$v = \frac{x}{t}$

$t = \frac{x}{v}$

Here$x = \phi$, then

$t = \frac{\phi}{v} = \frac{2\pi (6370*10^3)}{219}$

$t = 1.82*10^5s$

Therefore will take $1.82*10^5$ s or 506 hours, 19 minutes, 17 seconds