A man has a mass of 65kg on the Earth's surface. How far above the surface of the Earth would he have to go to "lose" 13% of his body weight?

You are asking how far up before g = .87 ge where ge is g at earth surface.

gravitational force is inversely proportional to distance squared.
we are at r radius, Re is earth radius.

so (r/Re)^2 = 1/.87 = 1.1494
r/Re = 1.07 or r = 1.0721 Re
then
r-Re = height above earth
=.0721 Re but Re = 6.4*10^6 meters approx
so
.0721*6.4*10^6 = .46*10^6 = 4.6*10^5 =460,000 meters

To calculate the distance above the Earth's surface that the man would have to go to "lose" 13% of his body weight, we need to understand the concept of gravitational force and the relationship between mass and weight.

Weight is the force exerted on an object due to gravity, and it is calculated by multiplying the mass of an object by the acceleration due to gravity. On the surface of the Earth, the standard acceleration due to gravity is approximately 9.8 m/s^2.

First, let's determine the man's weight on the Earth's surface. We can calculate his weight using the formula:

Weight = mass x acceleration due to gravity

Weight = 65 kg x 9.8 m/s^2

Weight ≈ 637 N (rounding to the nearest newton)

Now, the man wants to "lose" 13% of his body weight. To find the weight loss, we multiply the current weight by 0.13:

Weight loss = 0.13 x 637 N

Weight loss ≈ 82.81 N (rounding to the nearest newton)

Next, we need to find the distance above the Earth's surface where the weight loss occurs. The relationship between distance and weight loss is inversely proportional to the square of the distance. This is based on the inverse-square law of gravitational force.

So, we set up the equation as follows:

Weight loss on Earth's surface / Weight loss at new distance = (Distance on Earth's surface)^2 / (New distance)^2

82.81 N / Weight loss at new distance = (0 m)^2 / (New distance)^2

Simplifying the equation:

Weight loss at new distance = (82.81 N x (New distance)^2) / (0 m)^2

To isolate the new distance, we can rearrange the formula:

New distance = √((Weight loss at new distance x (0 m)^2) / 82.81 N)

New distance ≈ √((82.81 N x 0 m) / 82.81 N)

New distance ≈ √(0 m)

Therefore, the man would have to go an infinite distance from the Earth's surface to "lose" 13% of his body weight. In practical terms, it is not physically possible for him to achieve this weight loss without leaving the gravitational influence of the Earth.