[tex]\begin{gathered} mass=\text{ m= 1kg} \\ h_A=12\text{ m} \\ At\text{ point A} \\ E_A=E_{PA}+E_{KA,\text{ }}\text{ }E_{PA}=mgh_A\text{ , }E_{KA,\text{ }}=\frac{mv^2_A}{2} \\ E_A=mgh_A+\frac{mv^2_A}{2} \\ v_A=\text{ 0 m/s, Then} \\ E_A=E_{PA}=mgh_A \\ E_{PA}=\mleft(1\operatorname{kg}\mright)(9.81_{}m/s^2)(12m) \\ E_{PA}=117.72J \\ \text{The potential energy at point A is 117.72 J and kinetic energy is 0J} \\ \\ At\text{ point B} \\ E_A=E_B \\ E_{PA}=E_{PB}+E_{KB,\text{ }} \\ mgh_A=mgh_B+E_{KB,\text{ }} \\ E_{PB}=mgh_B \\ h_B=9m \\ E_{PB}=(1\operatorname{kg})(9.81_{}m/s^2)(9m) \\ E_{PB}=88.29J,\text{ then} \\ 117.72J=88.29J+E_{KB,\text{ }} \\ E_{KB,\text{ }}=117.72J-88.29J \\ E_{KB,\text{ }}=29.43J \\ \text{The potential energy at point B is }88.29J\text{ and kinetic energy is }29.43J \\ \\ At\text{ point C} \\ E_B=E_C \\ E_{PB}+E_{KB}=E_{PC}+E_{KC} \\ 117.72J=mgh_C+E_{KC\text{ }} \\ E_{PC}=mgh_C \\ E_{PC}=(1\operatorname{kg})(9.81_{}m/s^2)(6m) \\ E_{PC}=58.86J,\text{ then} \\ 117.72J=58.86J+E_{KC\text{ }} \\ E_{KC\text{ }}=117.72J-58.86J \\ E_{KC\text{ }}=58.86J \\ \text{The potential energy at point C is }58.86J\text{ and kinetic energy is }58.86J \\ \\ At\text{ point D} \\ E_C=E_D \\ E_{PC}+E_{KC}=E_{PD}+E_{KD} \\ 117.72J=mgh_D+E_{KD\text{ }} \\ E_{PD}=mgh_D \\ E_{PD}=(1\operatorname{kg})(9.81_{}m/s^2)(3m) \\ E_{PD}=29.43J \\ \text{Then} \\ 117.72J=29.43J+E_{KD\text{ }} \\ E_{KD\text{ }}=117.72J-29.43J \\ E_{KD\text{ }}=88.29J \\ \text{The potential energy at point D is }29.43J\text{ and kinetic energy is }88.29J \\ \\ At\text{ point E} \\ E_D=E_E \\ E_{PD}+E_{KD}=E_{PE}+E_{KE} \\ 117.72J=mgh_E+E_{KE\text{ }} \\ E_{PE}=mgh_E \\ E_{PE}=(1\operatorname{kg})(9.81_{}m/s^2)(0m) \\ E_{PE}=0J \\ \text{Then} \\ 117.72J=E_{KE\text{ }} \\ \text{The potential energy at point E is }0J\text{ and kinetic energy is 117.72}J \end{gathered}[/tex]
