the weight of an object varies inversely as the square of its distance from the center of the planet it is on. If a person weighs 180 pounds on a planet's surface, what is his weight 250 miles above the surface of the planet? The planet's radius is 7000 miles.
To solve this problem, we will use the inverse square relationship between weight and distance from the center of the planet. Let's use the formula:
Weight ∝ 1 / (distance^2)
First, let's relate the person's weight on the surface (180 pounds) with the distance from the planet's center (radius of the planet).
Weight = k / (distance^2)
Since we know that the person weighs 180 pounds on the surface of the planet, we can write the equation as:
180 = k / (7000^2)
Now, we need to find the value of the constant "k". Rearranging the equation, we get:
k = 180 * (7000^2)
k ≈ 8.82 * 10^9
Now we have the value of "k", we can find the weight of the person at a distance of 250 miles above the surface of the planet.
Weight = (8.82 * 10^9) / ((7000 + 250)^2)
Weight ≈ (8.82 * 10^9) / (7250^2)
Weight ≈ 180.069 pounds
Therefore, the person's weight 250 miles above the surface of the planet is approximately 180.069 pounds.