Answer
$$x=5.7 \mathrm{m}$$
Work Step by Step
At $x=7.0 \mathrm{m},$ the potential energy is $U_{3}=45 \mathrm{J}$ , which exceeds the initial total energy $E_{1} .$ Thus, the particle can never reach there. At the turning point, the kinetic energy equal zero. Between $x=5$ and 6 $\mathrm{m}$ , the potential energy is given by
$$
U(x)=15+30(x-5), \quad 5 \leq x \leq 6
$$
Thus, the turning point is found by solving $$37=15+30(x-5),$$ which yields $$x=5.7 \mathrm{m}$$
