$($a$)$

A spaceship is projected vertically upward from the Earth's surface with an initial speed of $7\mathrm{.}16$ 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.

m

$($b$)$

A meteoroid falls from a height of $1\mathrm{.}81107$ 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