A car travelling at 15 m/s comes to rest in a distance of 14 m when the brakes are applied.
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This question needs research to be answered. From the given information alone it can't be answered without making wild assumptions.
Ideally, you need to take a look at a distribution (or a histogram) of asteroid diameters, identify the "mode" of such a distribution, and find the corresponding diameter. That value will be the answer.
I am attaching one such histogram on asteroid diameters from the IRAS asteroid catalog I could find online. (In order to get a single histogram, you need to add the individual curves in the figure first). Eyeballing this sample, I'd say the mode is somewhere around 10km, so the answer would be: the diameter of most asteroid from the IRAS asteroid catalog is about 10km.
(a)
The total mechanical energy of the space probe must be constant, so we can write:
(1)
where
is the kinetic energy at the surface, when the probe is launched
is the gravitational potential energy at the surface
is the final kinetic energy of the probe
is the final gravitational potential energy
Here we have
at the surface, (radius of the planet),
(mass of the planet) and m=10 kg (mass of the probe), so the initial gravitational potential energy is
At the final point, the distance of the probe from the centre of Zero is
so the final potential energy is
So now we can use eq.(1) to find the final kinetic energy:
(b)
The probe reaches a maximum distance of
which means that at that point, the kinetic energy is zero: (the probe speed has become zero):
At that point, the gravitational potential energy is
So now we can use eq.(1) to find the initial kinetic energy: