Energy Problem Involving Spring Force

[angotta]

1. As a 1.7×104 jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 6.0×104 . If the spring stretches 31 to stop the plane, what was the plane's landing speed? (Answer in m/s)



2. Homework Equations
F_sp=k$$\Delta$$s where k is the spring constant and $$\Delta$$s is the change in position.
Also possibly the Equation for kinetic energy
K=1/2mv²
And also posibly
v_f²=v _i²+2a$$\Delta$$s
where v is velocity and a is acceleration

Also the conservation of energy and momentum equations are possible along with f=ma

The Attempt at a Solution

I found the spring force to be 1860000 N and then I lost where to go exactly. I tried to use F=ma to find acceleration, and then use kinematics (v_f²=v _i²+2a$$\Delta$$s) because v final should be zero, but I got the wrong answer. My incorrect answer was 82m/s.

 

[LowlyPion]

Maybe consider using the KE and PE of spring?

1/2*m*v² = 1/2*k*x²

v² = k*x²/m = 60,000*31²/17,000