A scientific probe of mass 50kg is projected radially outward from the Earth’s surface with an initial speed v0. Air resistance and the rotation of the Earth may be neglected. The probe rises to a maximum height h above the surface, where it momentarily comes to rest before falling back.
a. (i) Derive an expression connecting v0, h, G, M and RE (M and RE are the mass and radius of the Earth respectively).
b. (ii) Using your expression, calculate the initial speed required for the probe to reach a maximum height equal to twice the Earth’s radius (h=2RE).
c. (iii) Show that when h→∞, your expression reduces to the standard formula for the escape velocity from the Earth’s surface.