$1491.$ The $0\mathrm{.}5-$lb ball is shot from the spring device shown. Determine the smallest stiffness k which is required to shoot the ball a maximum distance s $=30$ in$.$ up the plane after the spring is pushed back $3$ in$.$ and the ball is released from rest. The four cords C and plate P keep the spring compressed $2$ in$.$ when no load is on the plate.

$14-91.$ The $0\mathrm{.}5-$lb ball is shot from the spring device

shown. Determine the smallest stiffness k which is required

to shoot the ball a maximum distance s$=30$in$.$ up the

plane after the spring is pushed back $3$ in$.$ and the ball is

released from rest. The four cords C and plate P keep the

spring compressed $2$ in $.$ when no load is on the plate.