How to solve this exercise in orbital mechanics; the moon stops in its orbit, what happens next?

As an exercise in orbital mechanics, suppose the moon were to suddenly stop orbiting Earth, and instead at time $t=0$ begin moving in the same direction as Earth so that their relative velocity were zero.

How could one go about calculating the answer to the following questions?

1. Would the Moon hit the Earth or not?
2. If it did, how long would it take?
3. If it didn't, what would its new orbit be like?
4. Does the answer depend on where the Moon is in its orbit?

Do we have to do detailed numerical integration to find the answer, or can we use some simple equations that involve energy and/or eccentricity to get an answer?