Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 207: 63b

$x= 0.9m$

$K + U = E_s + E_{th}$ $\frac{1}{2}mv^2 + mgx = \frac{1}{2}kx^2 + fx$ $(\frac{1}{2}\times 1800\times 7.4^2) + ( 1800\times 9.8 \times x) = (\frac{1}{2}\times 0.15 \times x^2 )+ 4400x$ $49284 + 17640x =75000 x^2 + 4400x$ $75000 x^2-17640x +4420x - 49284$=0 $75000 x^2-1322x - 49284$=0 Solving the quadratic eqn with a calculator: $x= 0.9m$