Question

Si la circunferencia de la Tierra es de 40 075 km ¿Con que rapidez se mueve una persona que se encuentra sobre el ecuador?

Answer 1

Answer: 463.83 m/s

Explanation:

The question in english is:

If the circumference of the Earth is 40075 km, At what speed does a person who is on the equator move?

We need to find the tangential speed $V$ of a person that is on the Earth's equator (assuming the Earth moves following a uniform circular motion) and we onle have the value of the circumference $C$ of the planet as data.

Since we assumed we are dealing with uniform circular motion, the tangential speed is expressed as:

$V=\frac{\omega D}{2}=\frac{\pi D}{T}$ (1)

Where:

$\omega$ is the angular frequency

$D$ is the diameter of the Earth

$T=24 h \frac{3600 s}{1 h}=86400 s$ is the period of revolution of the Earth (1 day)

On the other hand, the circumference $C$  of a sphere (assuming the Earth has this shape) is given by the following equation:

$C=2 \pi \frac{D}{2}$  (2)

Where $C=40075 km$ in this case.

Clearing $D$:

$D=\frac{C}{\pi}=\frac{40075 km}{\pi}$  (3)

$D=12756.268 km \frac{1000 m}{1 km}=12756268.69 m$  (4)

Substituting (4) in (1):

$V=\frac{\pi D}{T}$ (1)

$V=\frac{\pi (12756268.69 m)}{86400 s}$ (5)

Finally:

$V=463.831 m/s$ (6)