A robotic pool cue is designed to carefully impart enough energy to a cue ball for the precision needed when playing billiards. The robotic pool cue consists of a pool cue and a spring (with a spring constant k = 18 lb/in.) that can be depressed a specific distance x and suddenly released, providing a known amount of energy to the pool cue. Energy is stored in the spring until the cue is launched forward. The pool cue then impacts the cue ball (which has a weight of 6 ounces, or roughly 0.375 lb), imparting kinetic energy on the cue ball. The robotic pool cue configuration is shown below.

There are three energy states involved in this problem.

Energy State	Description	Spring Energy	KE of Pool Cue	KE of Cue Ball
1	Spring is at max compression, nothing is moving	Max	0	0
2	Spring is fully restored, pool cue is at maximum speed	0	Max	0
3	The pool cue impacts the cue ball, causing a change in momentum. Energy is transferred from the cue to the cue ball.	0	0	Max

The impact between the pool cue and the cue ball involves some energy loss (because it is not a perfectly elastic impact). As such, there is an efficiency less than 1 in the system. During one impact, the spring is compressed x = 1.13 in. Based on experimentation, it was determined that the efficiency of this system in converting spring energy to kinetic energy of the cue ball is approximately  = 0.89. What can you expect the speed of the cue ball to be after impact? (answer in ft/s)