Question

A city is located at 40 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city.

Answer 1

A city is located at 40 degrees north latitude. The radius of the Earth is equal to 3960 miles. So, the radius of the circular orbit made by that city will be,

r = 3960 × cos(40°)

  = 3960 × (0.7660444…)

 = 3033.5359947…

 ≈ 3033.536 miles

 

Earth rotates once every 24 hours. That is, the man who resides in the given city completes 1 round in 24 hours. So, the man subtends an angle of 2π in 24 hours.

 

The angular speed of a man who resides in this city will be,

w = θ/t

    = 2π/24 radians/hour

   = π/12 radians/hour

Consider the relation between linear speed (v) and angular speed (w),

v = rw

 

Substitute r = 3033.536 miles and w = π/12 radians/hour, the linear speed of a man who resides in this city will be,

v = (3033.536 miles) × (π/12 radians/hour)

   = 3033.536 × π/12 miles/hour

   = 794.177866292535… miles/hour

   ≈ 794.18 mi/h

 

Therefore, the linear speed of the man who resides in the city will be approximately 794.18 mi/h.

Therefore, the linear speed of the man who resides in the city will be approximately 794.18 mi/h.