1372.26 Joules
Explanation
Kinetic energy is the energy that an object possesses due to its motion, it is given by:
[tex]\begin{gathered} KE=\frac{1}{2}mv^2 \\ \text{where m is the mass of the object} \\ v\text{ is the velocity of the object} \end{gathered}[/tex]Potential energy is the stored energy an object has because of its position,it can be calculated using:
[tex]\begin{gathered} PE=\text{mgh} \\ \text{where m is the mass of the object} \\ g\text{ is the acceleration due to gravity} \\ h\text{ is the heigth (position)} \end{gathered}[/tex]The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another, so if we ignore the air resitance, we know the energy at A must be equal at the energy at B
so
[tex]\begin{gathered} KE_A+PE_A=KE_B++PE_B \\ \text{replace} \\ \frac{1}{2}(m)(v_1)^2+(m)(g)(h)=\frac{1}{2}(m)(v_2)^2+(m)(g)(h) \\ \frac{1}{2}(69kg)(5.8\frac{m}{s}_{})^2+(8kg)(9.8\frac{m}{s^2})(2.7)=\frac{1}{2}(m)(v_2)^2+(8kg)(9.8\frac{m}{s^2})(0) \\ 1160.58+211.68=\frac{1}{2}(8)(v_2)^2+0 \\ 1372.26=4(v_2)^2 \\ \text{divide both sides by 4} \\ \frac{1372.26}{4}=\frac{4(v_2)^2}{4} \\ 343.065=(v_2)^2 \\ \text{square root in both sides} \\ \sqrt{343.065}=\sqrt{(v_2)^2} \\ 18.52=v_B \end{gathered}[/tex]therefore, the kinetick energy would be
[tex]\begin{gathered} KE=\frac{1}{2}mv_b^2_{} \\ KE=\frac{1}{2}(8\text{ kg)}\cdot(18.52\frac{m}{s^2})^2 \\ KE=1372.26\text{ Joules} \end{gathered}[/tex]so, the answer is
1372.26 Joules
I hope this helps you
