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a) What must the force constant of the spring be?

b) What distance must the spring be compressed?

I don't really know how to approach this problem, since without the spring constant (k), you cannot find the distance the spring is compressed (x) and vice versa.

But, according to the problem,

0.5kx^2 + mgh = 0.5mv^2 +5mgh

0.5kx^2 = 0.5mv^2 + 4mgh

kx^2 = mv^2 + 8mgh

k = (mv^2 + 8mgh)/x^2

I know this has to be wrong because there are three unknowns, h, x, and k. Can someone help me approach this differently?