The earth has a radius of 6.38 106 m and turns on its axis once every 23.9 h.
A. What is the tangential speed (in m/s) of a person living in Ecuador, a country that lies on the equator?
(b) At what latitude (i.e., the angle θ in the drawing) is the tangential speed two-thirds that of a person living in Ecuador?
angular speed= 2PI/day
convert that to radians/sec
Then tangentialspeed= above ang;ular speed times radius
for any other latitude, multipy all that by cosine Latitude
To calculate the tangential speed of a person living in Ecuador (on the equator), we can use the formula for tangential speed:
Tangential Speed = Radius x Angular Speed
(A) First, we need to find the angular speed of the Earth. We are given that the Earth turns on its axis once every 23.9 hours. To convert this into seconds, we multiply by 60 (minutes per hour) and another 60 (seconds per minute):
Angular Speed = (2π radians) / (Time in seconds)
= (2π radians) / (23.9 hours * 60 minutes/hour * 60 seconds/minute)
Next, we calculate the radius of the Earth:
Radius of Earth = 6.38 * 10^6 m
Finally, we can substitute these values into the formula to find the tangential speed:
Tangential Speed = (6.38 * 10^6 m) * [(2π radians) / (23.9 hours * 60 minutes/hour * 60 seconds/minute)]
(B) To find the latitude at which the tangential speed is two-thirds that of a person living in Ecuador, we can set up the following equation:
Tangential Speed at Latitude θ = (2/3) * Tangential Speed in Ecuador
We can rearrange this equation to solve for θ:
θ = arccos [(2/3) * Tangential Speed in Ecuador / Tangential Speed at Latitude θ]
We can use the tangential speed calculated in part (A) and substitute it into the equation to find θ.