A spaceship is projected vertically upward from the Earth's surface with an initial speed of $8\mathrm{.}11$ km$/$s$,$ but unfortunately does not have a great enough speed to escape Earth's gravity. What maximum height does the spaceship reach $($in m$)?$ Ignore air resistance.

Apply the conservation of mechanical energy, where

vf $=0.$

You will need to know the radius and mass of the Earth. Be careful with your signs when writing the potential energy expressions. Note that you can use energy conservation to write the initial potential energy of the system in terms of the escape velocity. Solve your equation for h$.$ m

$($b$)$

A meteoroid falls from a height of $1\mathrm{.}51107$ m above the surface of the Earth. What is the speed $($in m$/$s$)$ when the meteorite hits the Earth? Assume the meteoroid is initially at rest with respect to the Earth. $($Note that a meteorite is a meteoroid that makes it to Earth's surface.$)$

m$/$s