I\'m having trouble with an exercise. A long range missile is launched from the

Question

I'm having trouble with an exercise. A long range missile is launched from the surface of the Earth, with initial velocity v=(v_r, v_theta) in POLAR COORDINATES, with the origin of the polar coordinate system at the center of the Earth. Without taking into account the rotation of the Earth or friction, but using the full gravitational expresion (GMm/R2), I'm asked to find an equation for the max height over the surface reached by the missile.

I'm tempted of doing this with conservation of mechanical energy, but the problem is that the missile is not launched straight up, because it has a component in the theta direction.

Any help? Thanks.

Explanation / Answer

Component of velocity in vertically upward direction is v_r*sin(v_theta), and using it in kinetic energy formula and equating with potential energy at the top, that is, maximum height you will get your answer.

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