Cannoneer and Foxhole

A cannoneer is trying to hit a foxhole with a mortar. The foxhole is 384 m horizontally away from the mortar mouth. The mortar fires at the fixed angle of 53$^\circ$ but has a charge that can be adjusted so that its mortar shells come out of the mortar with any desired velocity (within reason). (Note: 345 triangle, $\sin(53) = 0.8$, $\cos(53) = 0.6$)

a) Find the initial velocity required to hit the foxhole.

b) How long should the fuse on the mortar be set for (assuming that one wishes it to detonate just as it reaches the ground at the other end.