Question

What is the speed of a point on the earth's surface located at 3/43/4 of the length of the arc between the equator and the pole, measured from equator

Answer 1

`v=177.95m/s`

Step-by-step explanation:

First, determine circle's radius between Earth's pole and the location. This can be calculated as:

`r=R_e_a_r_t_hCos(90(3)/(4))\\R_e_a_r_t_h=6.37*10^6m\\r=6.37*10^6* Cos67.5\textdegree\\r=2,437,693.46m\\`

The angular speed of earth is constant and is :

`w=(2\pi)/(T)=(2\pi)/(24* 3600)\\=7.3*10^(-5)rad/s`

Velocity is:

`v=wr\\=7.3*10^(-5)* 2,437,693.46\\v=177.95m/s`