Problem 1: A rocket of mass m is launched from the surface of the Earth. The rocket is subject only to the effects of gravity (there are no other forces acting on the rocket). Assuming that the rocket travels in a straight line away from the Earth as shown.
(a) Write the equation of motion of the rocket. Take the mass of the Earth as Me and the radius of the carth tobe Re. The force of attraction from the carth can be expressed as a force acting on the rocket towards thecenter of the carth with magnitude F, = mge where g is the usual gravity acceleration.
(b) The initial velocity with which the rocket must be launched from the surface of the earth (ie, X, = R) so that it escapes the gravitational attraction of the earth. Note that this requires integration of the equation to find v as a function of x and then substituting v = 0 as x
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