There are a number of possible ways to do this but the easiest is to model your arrow as a mesh (it needs to be a fairly dense mesh to stand up to the deformations) Now draw a spline line that represents the path of the animation. From here simply apply a path deform world space modifier to the arrow. you will see a pick path button to select your spline. Now click the move to path button. From here you may need to change which axis the arrow is deforming along. Now you can animate the percent and stretch to get your effect.