Elastic Potential Energy and Hooke's Law Problem

[y201]

Homework Statement

A small truck is equipped with a rear bumper that has a spring constant of 800,000 N/m. the bumper can be compressed up to 15cm without causing damage to the truck. What is the maximum velocity with which a solid 1000-kg car can collide with the bumper without causing damage to the truck?

Homework Equations

Kinetic Energy=(1/2)(m)(v^2)
Elastic Energy=(1/2)(k)(x^2)

The Attempt at a Solution

I tried to make those two equations equal to one another and then isolate for "v" and solve for it. however, i got the wrong answer. the answer at the back of the book is 34 m/s. this problem is based on elastic potential energy and hooke's law. all help is appreciated.

 

[Birkeland]

Did you convert the 15cm to 0.15m? Otherwise the process you described is correct.

Actually, I just did the problem backwards. Using their "correct answer" of 34 m/s means the bumper must move 1.5 m, not 0.15. Basically the back of you book is wrong.

 

[y201]

thanks a lot birkeland for your help.
what did you get as the right answer?

 

[y201]

Did you convert the 15cm to 0.15m? Otherwise the process you described is correct.

Actually, I just did the problem backwards. Using their "correct answer" of 34 m/s means the bumper must move 1.5 m, not 0.15. Basically the back of you book is wrong.

what answer did you get using the 0.15m?