A body with speed v is projected from the surface of the earth(mass M & radius R). Find the maximum distance from the earth that this body reaches before returning back to earth, as a function of the initial speed v, M, R and the gravitational constant G
This question tests the students' understanding on conservation of energy, gravitational potential and algebraic manipulation.The first step is identifying that the principle to use is the conservation of energy:K.E. initial + P.E. intial =K.E. final + P.E. final .When you substitute in the expressions for the energies this becomes: 1/2 m v2 -GMm/R = 1/2 m v2final -GMm/rfinal. Another key step in solving it, is recognising that the maximum height occurs at the point where vfinal =0. The rest is just rearranging so that you have r in terms of v,G,M,R until you reach: r =2GMR/(2GM-Rv2). From this expression, a lot of useful information can be gathered, for example one can derive the escape velocity of a body from earth
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