I want to drop a ball in a vacuum from 10 miles high to Earth's surface and calculate it's free-fall time. This question is more involved than simply using $$x = \frac{1}{2}gt^2$$ because g is not constant.
I know how to calculate the final velocity of the object falling... Just integrate Newton's gravity equation from R+h to R to get the amount of work done by gravity to pull the object a distance of h (being 10 miles), setting it equal to $$\frac{1}{2}mv^2$$ and solving for v.
But, how do I calculate the free-fall time? It's not clear to me because g is always changing.
I know how to calculate the final velocity of the object falling... Just integrate Newton's gravity equation from R+h to R to get the amount of work done by gravity to pull the object a distance of h (being 10 miles), setting it equal to $$\frac{1}{2}mv^2$$ and solving for v.
But, how do I calculate the free-fall time? It's not clear to me because g is always changing.