At what distance from the earth's surface with a mass of 5.0kg be just 45.0N in weight.

HELP

To solve this problem, we need to use the equation for gravitational force:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects being considered (in this case, the mass of the Earth and the mass of the object)
r is the distance between the centers of the two masses

We can rearrange the equation to solve for r:

r = sqrt((G * m1 * m2) / F)

Given:
m1 = mass of the Earth = 5.972 × 10^24 kg
m2 = mass of the object = 5.0 kg
F = 45.0 N

Let's substitute these values into the equation:

r = sqrt((6.674 × 10^-11 N m^2 / kg^2 * 5.972 × 10^24 kg * 5.0 kg) / 45.0 N)

Now, let's calculate:

r = sqrt((3.9817 × 10^14 N m^2 * kg^2) / 45.0 N)

r = sqrt(8.8488 × 10^12 m^2)

r ≈ 2.973 × 10^6 meters

Therefore, the object would be approximately 2.973 × 10^6 meters, or 2,973 kilometers, from the Earth's surface when it weighs 45.0N.