Can someone help me with this practice problem for Physics?

Question

Calculate the linear speed due to the earth's rotation for a person at a point on its surface located at 40 degrees N latitude. The radius of the earth is 6.40 x 10^6 m.

Answer 1

V = r*ω

r = Re*cos40° = 4.903E6 m

ω = (1rev/24hr)*2πrad/rev*(1hr/3600sec) = 72.72E-6 rad/sec

V = 4.903E6*72.72E-6 = 356.5 m/s

Answer 2

The person makes one  orbit of a circle in 24 hours.

At latitude 40 deg. (north or South), the person will move in a circle of radius:-

                                 R * cos (40)

                         =    6.40 E+06 * 0.766   =   4.902 E+06 m

The circumference of this circle is  2 & pi * R

                            =   2 * 3.14156 * 4.902 E+06

                            =   3.08  E +07 m

This distance is covered in 24 hours,  (24 * 3600 seconds)

  Speed   =-  distance / time    =   3.08 E +07 / 24 * 3600

                          Speed     =      356.48

                                        say,   360 m / sec.