# A man weighs 750.0 N on Earth at what altitude will he weigh 187.5 N?

solve for alt.

## To find the altitude at which a man weighs 187.5 N, we need to make use of the concept of gravitational force and the formula for weight. The weight of an object can be calculated using the formula:

Weight = mass * acceleration due to gravity

On Earth, the standard acceleration due to gravity is approximately 9.8 m/s².

Let's determine the mass of the man first. To do this, we can use the formula:

Weight = mass * acceleration due to gravity

Rearranging the formula to solve for mass:

mass = Weight / acceleration due to gravity

Given that the man weighs 750.0 N on Earth, we can calculate his mass:

mass = 750.0 N / 9.8 m/s²

mass ≈ 76.53 kg (rounded to two decimal places)

Now that we know the mass of the man, let's determine the altitude at which he will weigh 187.5 N.

The gravitational force at any given altitude is given by the formula:

Weight = mass * acceleration due to gravity

Therefore, we can calculate the altitude when the weight is 187.5 N:

altitude = (Weight / acceleration due to gravity) - radius of the Earth

However, we need to consider that as altitude increases, the distance from the center of the Earth (radius) increases. The radius of the Earth varies depending on the reference used, but for simplicity, we can consider it as approximately 6,371,000 meters (6,371 km).

Substituting the values into the formula above:

altitude = (187.5 N / 9.8 m/s²) - 6,371,000 m

altitude ≈ -6,370,810.2 m (rounded to one decimal place)

The negative value indicates a depth rather than an altitude. Therefore, at an altitude of approximately 6,370,810 meters above the surface of the Earth, the man will weigh 187.5 N.