Download Escape speed problem worksheet

ESCAPE SPEED WORKSHEET
1. Calculate the amount of energy required to escape from Earthʼs moon relative to that
required to escape from the Earth.
2. Zero, a hypothetical planet, has a mass of
, a radius of
,
and no atmosphere. A 10 kg space probe is to be launched vertically from its surface.
a. If the probe is launched with an initial energy of
energy when it is
, what will be its kinetic
from the center of Zero?
b. If the probe is to achieve a maximum distance of
from the center of
Zero, with what initial kinetic energy must it be launched from the surface of Zero?
3. A rocket is accelerated to speed
upward.
a. Show that it will escape from Earth.
near Earthʼs surface, and it coasts
b. Show that very far from Earth its speed will be
.
4. Planet Roton, with a mass of
and a radius of
, gravitationally
attracts a meteorite that is initially at rest relative to the planet, at a great enough
distance to take as infinite. The meteorite falls toward the planet. Assuming the planet is
airless, find the speed of the meteorite when it reaches the planetʼs surface.
5. A projectile is fired vertically from the Earthʼs surface with an initial speed of
Neglecting air drag, how far above the surface of Earth will it go?
.