A sensitive gravimeter is carried to the top of New York\'s new One World Trade

Question

A sensitive gravimeter is carried to the top of New York's new One World Trade Center where its reading for the acceleration of gravity is 1.67 mm/s^2 lower than at street level. Find the building's height. Express your answer to two significant figures and include the appropriate units. A projectile is fired from a very powerful cannon vertically upward from Earth's surface at an initial speed of 5.5 km/s. The mass of the earth is 5.97 x 1024 kg and the radius of the earth is 6370 km. What is its maximum altitude (above the surface of the Earth)? Assume that air resistance is negligible. Express your answer using two significant figures.

Explanation / Answer

variation of acceleration due to gravity with altitude is given as

g' = g (1 - 2h/R)

g - g' = 2gh/R                    R = radius of earth , h = height above the surface

1.67 x 10-3 = 2 (9.8) h / (6.37 x 106)

h = 542.75 m

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