Solve the Problem $$g ( h ) = \frac { 3.99 \times 10 ^ { 14 } } { \left( 6.374 \times 10 ^ { 6 } + h \right) ^ { 2 } }$$

question 339

Essay

Solve the problem.
-The acceleration due to gravity g (in meters per second per second) at a height h meters above sea level is given
by $$g ( h ) = \frac { 3.99 \times 10 ^ { 14 } } { \left( 6.374 \times 10 ^ { 6 } + h \right) ^ { 2 } }$$ where $$6.374 \times 10 ^ { 6 }$$ is the radius of Earth in meters. Death Valley in California is 86 m
below sea level.
a) Find the value of g(h) at Death Valley to four decimal places.
b) Compare the value in (a) to the value of g(h) at sea level.