An exercise from The Physics of Quantum Mechanics by James Binney and David Skinner

I am now tying to solve this question. I cn find out the probability of trasmission and rebouncing for that $\alpha$ particle. However, how can I use the condition "speed~ $c/3$"? Should I consider states of well defined momentum? I am looking forward to getting an idea about how to approach this question.
Also, why do we want to find $W$? Should I consider states with well defined parity?