the innerspring mattress on your bed is held up by 35 vertical springs.?

Question

Each having a spring constant of 5000 N/m
A 41kg person jumps from a 1.9m platform onto the innersprings.
the accel of gravity is 9.8m/s^2
assume the springs were initially unstretched and that they stretch equally .

Determine the stretch of each of the springs.

Answer 1

There's an unrealistic assumption here that all the springs compress equally. However, it makes the problem soluble, so:
x = spring deflection
k = 35 * 5000 N/m
PE1 = mgh = mg(1.9+x)
PE2 = kx^2/2
PE1 = PE2 ==> k/2*x^2 - mg*x - 1.9mg = 0
This is a quadratic in x. Solve it and take the positive root.