Explanation:
Given that,
An object in free fall will fall d feet in t seconds, where d and t are related by the algebraic model as :
..........(1)
(a) We need to find the time taken by the object to fall 1148 ft. Put this in equation (1) as :
t = 8.47 seconds
(b) If the object is in free fall for 18.5 sec after it is dropped, then the height of the object is given by :
d = 5476 ft
Hence, this is the required solution.
(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: