59. Acceleration Due to Gravity. The acceleration due
to gravity is often denoted by g in a formula such as
S = 5gt, where S is the distance that an object falls
in time t. The number g relates to motion near the
earth's surface and is generally considered constant.
In fact, however, g is not constant, but varies slightly
with latitude. Latitude is used to measure north-south
location on the earth between the equator and the
poles. If o stands for latitude, in degrees, g is given
with good approximation by the formula
g = 9.78049(1 + 0.005288 sino - 0.000006 sin-20),
where g is measured in meters per second per second
at sea level.
a) Chicago has latitude 42°N. Find g.
b) Philadelphia has latitude 40°N. Find g.
c) Express g in terms of sin o only. That is, eliminate
the double angle.