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"The Great Sandini is a circus performer with mass 60.0 kg who is shot from a cannon (actually a spring gun). You don't find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1400 N/m that he will compress with a force of 4800 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 35.0 N during the distance of 4.90 m that he moves in the barrel. At what speed will he emerge from the end of the barrel, a distance 2.60 m above his initial rest position?"

Now, i used hooke's law to find the distance he will travel while still touching the spring.

F = k * x

4800 N = 1400 N/m * x

3.43 m = x

Then, i used the conservation of energy theorem,

Potential(i) + Kinetic(i) + W(friction) = Potential(f) + Kinetic(f)

1/2*k*x^2 + 1/2*m*v^2 + (F*d) = m*g*h + 1/2*m*v^2

1/2*(1400)*(3.43)^2 + 1/2*(60)*(0)^2 + (35)(4.9) = (60)*(9.8)*(2.6) + 1/2*(60)*v^2

8240 J + 172 J = 1530 J +30*v^2

229 m^2/s^2= v^2

15.1 m/s = v

I submitted this answer to mastering physics and it told me i was close and that i may have made a rounding or significant figures error. i submitted 15.2 just to check, and i got the same feedback, maybe it's 15.0?

I think i may have done hooke's law wrong, and that in fact the distance should be twice what i found, using F*x = 1/2*k*x^2, but i only have one attempt left and i want to be sure. Using the second spring potential energy formula and plugging it into the conservation of energy theorem, my answer is 32.4 m/s.