S$13\mathrm{.}16$: An object is released from rest at an altitude h above the surface of the Earth. $($a$)$

Show that its speed at a distance r from the Earth's center, where $+$h$,$ is $=$

$2$

$1$

$1$

$$ h $.($b$)$ Assume the release altitude is $500$ km$.$ Perform the integral $$

$=$

$=$

$$

$$

$$ to find the time of fall as the object moves from the release point to

the Earth's surface. The negative sign appears because the object is moving opposite to

the radial direction, so its speed is v $=-$dr$/$dt$.$ Perform the integral numerically. You

may want to use a mathematical computational program such as Wolfram Alpha

Integral.