Question

The acceleration of gravity as a function of elevation above sea level is given by g =
9.807 - 3.32x10-6 z , where g is in m/s2 and z is in meters. Find the height, in
kilometers, above sea level where the weight of a person will have decreased by
a. 3 percent b. 10 percent.

Answer 1

we know that the weight is mass times the acceleration due to gravity. mass does not change place to place. hence percentage decrease in acceleration due to gravity is same as the percentage decrease in weight.

a)

The acceleration of gravity as a function of elevation above sea level is given by

g = 9.807 - (3.32 x 10⁻⁶) z

given that : g = 9.807 - (0.03) (9.807)

so

9.807 - (3.32 x 10⁻⁶) z = 9.807 - (0.03) (9.807)

(3.32 x 10⁻⁶) z = (0.03) (9.807)

z = 88617.5 m = 88.6 km

b)

The acceleration of gravity as a function of elevation above sea level is given by

g = 9.807 - (3.32 x 10⁻⁶) z

given that : g = 9.807 - (0.10) (9.807)

so

9.807 - (3.32 x 10⁻⁶) z = 9.807 - (0.10) (9.807)

(3.32 x 10⁻⁶) z = (0.10) (9.807)

z = 295392 m = 295.4 km

Answer 2

Answer:

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