Question

A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 0.0075 m/s2 less than that at sea level (gsealevel = 9.83 m/s2). Part A: What is the observatory's altitude? Assume Rearth = 6.37 �� 106 m.

Answer 1

The observatory's altitude can be determined by finding the difference in free-fall acceleration between the observatory and sea level. The altitude is approximately 39.13 meters.

Step-by-step explanation:

To determine the observatory's altitude, we first need to find the difference between the free-fall acceleration at the observatory and at sea level. The question states that the observatory's free-fall acceleration is 0.0075 m/s² less than that at sea level, which is 9.83 m/s². This means the observatory's free-fall acceleration is 9.83 m/s² - 0.0075 m/s² = 9.8225 m/s².

Next, we can use the equation for free-fall acceleration:

a = g(Rearth / (Rearth + h))

where a is the observed acceleration, g is the acceleration due to gravity at sea level, Rearth is the radius of the Earth, and h is the altitude of the observatory. Solving for h, we get:

h = Rearth((g/a) - 1)

Substituting the given values, we have:

h = (6.37 x 10⁶ m)((9.83 m/s²) / (9.8225 m/s²) - 1) = 39.13 m

Therefore, the observatory's altitude is approximately 39.13 meters.