Final answer:
To find the height where a person's weight decreases by a certain percentage, we use the formula for gravitational force and the fact that this force decreases as you move away from the center of the Earth. A 3% decrease corresponds to a height of approximately 888 km, and a 10% decrease to approximately 2900 km.
Step-by-step explanation:
The answer to this question lies in the concept of gravitational force, which changes with altitude. The force of gravity decreases with distance from the center of the Earth. Therefore, as one goes higher above sea level, their weight (which is force due to gravity) decreases.
To calculate the exact height, we need to use the formula for gravitational force, F = mg = G * m1 * m2 / r^2, where G is the gravitational constant, m1 and m2 the masses (of the Earth and person respectively), and r is the radius. By setting F1/F2 = r2^2/r1^2 where F1 and F2 are the weights at sea level and at the desired height and r1 and r2 are the Earth's radius and the distance from the Earth's center at the desired height, we can solve for r2.
(a) For 3% decrease, we have F2 = 0.97 * F1. Solving for r2, we find the height above sea level to be approximately 888 km.
(b) For 10% decrease, F2 = 0.9 * F1. Solving for r2, we get the height to be about 2900 km. Please note, this is a simplification as the Earth is not a perfect sphere and air resistance, among other factors, can influence weight.
Learn more about gravity and weight