HRW p. 93 # 69.  Solution
Diagram
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N and S mark the north and south poles, respectively.  Theta is, of course, necessarily 40 degrees.
r is the distance from a point on the 40-degree latitude circle to the rotation axis of the earth.
Quantities Given and Needed
6
Radius of the earth	R6.37.10.m
(see table on front cover)
p
40.
Theta	q
180
Radius of latitude circle	rR.sin(q)
Circumference of latitude	c2.p.r	[r, not R]
circle
velocity of person on 
v	=?
latitude circle
Acceleration of person on	a	wanted
latitude circle
Techniques
The person is being carried around a circle by the rotation of the earth.  Hence we need to analyze the centripetal acceleration in circular motion.  To do this we need the speed, which is given by the distance travelled divided by the time [definition of speed].  But the distance travelled is once around the circle per day.  So The person is being carried around a circle by the rotation of the earth.  Hence we need to analyze the centripetal acceleration in circular motion.  To do this we need the speed, which is given by the distance travelled divided by the time [definition of speed].  But the distance travelled is once around the circle per day.  So
Details
2
v a	rR.cos(q)
r
r v2.p.
1.day
Hence
2
r 2.p.
1.day a
r
2R.cos(q)
a4.p.
2
day
2	m
a=0.03msec	compared to	g9.8.	;  reasonable in size.
2
sec