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(a) With what speed does the projectile leave the barrel of the cannon?

(b) At what point does the ball have maximum speed?

(c) What is this maximum speed?

2. Homework Equations

d = delta/change in

dK - dPE (due to gravity) - dPE (due to spring) = Wf

.5m(Vf)^2 - .5m(Vi)^2 + mgh - mghi + .5k(xf)^2 - .5k(xi)^2 = -fd

(assuming that the only one i need?)

**3. The Attempt at a Solution**

I've tried going over this a couple of times and have no idea how to get the answer to (a) which is 1.40 m/s. Since there's no PE due to gravity since its all in the horizontal, i can eliminate dPEg, and since it starts at rest i can eliminate Ki. I think i can also get rid of the final x position of the spring since after the cannon fires the spring returns to its unstretched position? which would leave me with:

.5m(Vf)^2 - .5k(xi)^2 = -fd

I'm assuming with it being compressed and having xf being 0, that xi = -.05 m and since it travels .15 m, that d = .1 m, not .15 m. since you're given everything else when you rearrange it to isolate Vf you get:

Vf = sqrt[((k(xi)^2) - (2fd)) / m]

but when i do this i get Vf = .505 m/s.

I've gone over it and looked through the book again and again but i have to be missing something. Any help would be appreciated as I have a midterm on the material tomorrow morning. Also, my first post so if its difficult to read I apologize. Thanks.

I've tried going over this a couple of times and have no idea how to get the answer to (a) which is 1.40 m/s. Since there's no PE due to gravity since its all in the horizontal, i can eliminate dPEg, and since it starts at rest i can eliminate Ki. I think i can also get rid of the final x position of the spring since after the cannon fires the spring returns to its unstretched position? which would leave me with:

.5m(Vf)^2 - .5k(xi)^2 = -fd

I'm assuming with it being compressed and having xf being 0, that xi = -.05 m and since it travels .15 m, that d = .1 m, not .15 m. since you're given everything else when you rearrange it to isolate Vf you get:

Vf = sqrt[((k(xi)^2) - (2fd)) / m]

but when i do this i get Vf = .505 m/s.

I've gone over it and looked through the book again and again but i have to be missing something. Any help would be appreciated as I have a midterm on the material tomorrow morning. Also, my first post so if its difficult to read I apologize. Thanks.