Escape speed on Mars is 5.0km s−1. A probe is launched radially outward from the Martian surface with an initial speed of 4.0km s−1. Mars has mass MM=6.4×1023kg and radius RM=3.4×106m.
(i) Deduce a general expression for the farthest distance rmax (measured from the planet’s centre) attained by a body projected radially outward with initial speed u that is less than the planet’s escape speed.
(ii) Using the data above, calculate the numerical value of rmax for the probe and hence find its greatest height above the Martian surface.
(iii) If the probe falls back to the surface along the same radial line, determine its speed just before impact, neglecting the Martian atmosphere.