How many arrows of force would be needed in a free body diagram of a rocket taking off from the moon? ignore any solar system objects other than the moon itself. four two three one

So, here you are asking how many forces are acting on the rocket, because each force has an arrow.

the forces acting on the rocket are: The moons gravity, and the force of the propulsion of the rocket (if we assume there are no other objects which gravity will affect our problem).

so only  2 forces, you can use 2 arrows to diagram it. But this two forces are in the same direction (but are opposite), so you can simplify the diagram by adding the two forces, and write it with only one arrow.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y