How much do the bed springs stretch when a person jumps on them?

[vinnyzwrx]

Homework Statement

The innerspring mattress on your grandmother’s bed is held up by 20 vertical springs, each having a spring constant of 5000 N/m. A 48 kg person jumps from a 1.95 m platform onto the innersprings.
The acceleration of gravity is 9.8 m/s2 .
Assume: The springs were initially un- stretched and that they stretch equally (typical old fashioned bed).
Determine the stretch of each of the springs. Answer in units of m.

Homework Equations

consevation of mechanical energy using spring equation, 1/2kx²

The Attempt at a Solution

im not really sure how to setup the conservation of energy equation... if i have it right here then i should solve for y, but i don't see how to do that algebraically. i will always end up with a y on either side. unless I'm supposed to apply the quadratic formula... nope, still a wrong answer. am i setting up the conservation of energy equation right?

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[vinnyzwrx]

should the spring constant be multiplied by 20 to compensate for the 20 springs, or should the answer be divided by 20?

i don't see where i went wrong in my math...

 

[vinnyzwrx]

edited