$(15$ points$)$ In a weak moment you have volunteered to be a human cannonball at an amateur charity circus. The "cannon" is actually a $3$ foot diameter tube with a big stiff spring inside which is attached to the bottom of the tube. A smali seat is attached to the free end of the spring. The Ringmaster, one of your soon to be ex$-$friends, gives you your instructions. He tells you that just before you enter the mouth of the cannon, a motor will compress the spring to $\frac{1}{10}$ its normal length and hold it in that position. You are to gracefully crawl into the tube and sit calmly in the seat without holding on to anything. The cannon will both be raised to an angle such that your speed through the air at your highest point is $10f\frac{t}{s}.$ When the spring is released, neither the spring nor the chair will touch the sides of the $12$ foot long tube. After the drum roll the spring is released and you will fly through the air with the appropriate sound effects and smoke. With the perfect aim of your gun crew, you will fly through the air over a $15$ foot wall and land safely in the net You are just a bit worried and decide to calculate how high above your starting position you will be at your highest point. Before the rehearsal, the cannon is taken apart by maintenance and you can see the spring, which was removed from the cannon. When the spring is hanging straight down with one end attached to the ceiling, you determine that it is $10.$ feet long. When you hang on its free end, without touching the ground, it stretchess by $1\mathrm{.}5$ ft$.$ Is it possible for you to make it over the wall?