| Date | May 2016 | Marks available | 1 | Reference code | 16M.2.HL.TZ0.5 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | Outline | Question number | 5 | Adapted from | N/A |
Question
Outline what is meant by escape speed.
A probe is launched vertically upwards from the surface of a planet with a speed
\[v = \frac{3}{4}{v_{{\rm{esc}}}}\]
where vesc is the escape speed from the planet. The planet has no atmosphere.
Determine, in terms of the radius of the planet R, the maximum height from the surface of the planet reached by the probe.
The total energy of a probe in orbit around a planet of mass M is \(E = - \frac{{GMm}}{{2r}}\) where m is the mass of the probe and r is the orbit radius. A probe in low orbit experiences a small frictional force. Suggest the effect of this force on the speed of the probe.
Markscheme
speed to reach infinity/zero gravitational field
OR
speed to escape gravitational pull/effect of planet’s gravity
Do not allow reference to leaving/escaping an orbit.
Do not allow “escaping the atmosphere”.
«kinetic energy at take off» =\(\frac{9}{{16}} \times \frac{{GMm}}{R}\)
kinetic energy at take off + «gravitational» potential energy = «gravitational» potential energy at maximum height
OR
\(\frac{9}{{16}} \times \frac{{GMm}}{R} - \frac{{GMm}}{R} = - \frac{{GMm}}{R}\)
solves for r and subtracts R from answer =\(\frac{{9R}}{7}\)
Award [0] for work that assumes constant g.
energy reduces/lost
radius decreases
speed increases
Do not allow “kinetic energy reduces” for MP1
