You$$re working in mission control for an interplanetary space probe. A trajectory correction calls for a rocket firing that imparts an impulse of

$5$

$.$

$64$

$$

N$$s

$.$

If the rocket$$s average thrust is

$135$

$$

mN

$,$

how long should the rocket fire?

$$

mg

$.$

The more massive piece moves horizontally at

$47$

$$

cm$/$s

$.$

Describe the motion of the second piece