Which acceleration to use - Coriolis? 
In this diagram, water is being ejected from a sprinkler, rotating at speed $\dot\theta = 2 rad/s$ and angular acceleration $\ddot\theta = 3 rad/s^2$ .
Water is flowing the the sprinkler at $3m/s$. In order to find the acceleration of the water, I know that the coriolis acceleration will act perpendicular to the pipe with $a_c = 2\dot{r}\dot\theta$. But im unsure as to why this acceleration is used, as opposed to the acceleration component of a particle in curvilinear motion that is $a_\theta = \ddot\theta r + 2\dot{r}\dot\theta$
They both seem to act in the same direction but im not sure why coriolis is used instead of the other one
 A: Firstly note that corriolis force acts tangentially to centrifugal or centripedal acceleration.  
The centripetal force is that required to constrain matter to move in circular motion.
Although the sprinkler nozzle is moving this way, the water inside it is not radially constrained.  
Centrifugal force is that experienced by matter in a rotating frame of reference. But the calculations are being made in the frame of reference of the garden, not the nozzle.   
The coriolis force is experienced when moving radially in a rotating frame of reference. An object tries to conserve energy and maintain constant speed as it goes around, but the length of the circumference varies with radius. The angular velocity must vary in order to maintain constant speed.
The hole in the nozzle allows the water to move freely radially - but the walls of the nozzle constrains/accelerates it tangentially to the arc of motion. 
The water experiences an equal and opposite reaction to the coriolis force - that is although to conserve energy (velocity) it would have reducing $\dot \theta$ as it moves along the nozzle, but it is constrained to speed up as because the end of the nozzle is rotating faster.
