A projectile is fired from the earth with the aim at getting into space. The velocity
(v)
of the projectile is described by the following ODE:
(dv)/(dr)=-(gR^(2))/(vr^(2))
Where
r
is the distance from the centre of the earth to the projectile,
g
is the earth's gravity and
R
is the radius of the earth. The initial velocity is denoted
v_(0)
and occurs on the surface of the earth. a) Solve the above ODE and explicitly express velocity
(v)
as a function of
r
b) Show with justification that the minimum velocity required to ensure that the object does not return to earth is given by:
v=\sqrt(2gR)