a 180 lb person climbs a ladder to a point which is two times the radius of the earth high. how much does he weigh there?
To calculate the weight of a person at a different height from the Earth's surface, we need to consider the gravitational force acting on them. The force of gravity diminishes as you move away from the Earth's surface.
To determine the person's weight at a height of two times the radius of the Earth, we can use the following formula:
Weight at a height = Weight on the Earth's surface * (Radius of Earth / (Radius of Earth + Height))
First, let's determine the weight of the person on the Earth's surface. You mentioned the person weighs 180 pounds. So, the weight on the Earth's surface is 180 pounds.
The radius of the Earth is approximately 3,963 miles or 6,378 kilometers. We'll use the radius in the same unit as the height, so let's convert 2 times the radius of the Earth into the equivalent units.
If we assume the radius is in miles (which is the more common unit), then the height would be (2 * 3,963) miles = 7,926 miles.
Now, we can substitute these values into the formula to calculate the weight at that height:
Weight at height = 180 * (3963 / (3963 + 7926))
Let's solve this equation:
Weight at height = 180 * (3963 / 11889)
Weight at height ≈ 60 pounds
Therefore, the person would weigh approximately 60 pounds when they climbed to a point two times the radius of the Earth.