Chapter 8 - Potential Energy and Conservation of Energy - Problems and Conceptual Exercises - Page 248: 49

$134KJ$

We know that $W_{nc}=W_{nc_1}+W_{nc_2}=E_f-E_i$ $\implies W_{nc_1}+W_{nc_2}=(K.E_f+U_f)-(K.E_f+U_i)=\Delta K.E+mg(y_f-y_i)$ $\implies \Delta K.E=W_{nc_1}+W_{nc_2}-mg(y_f-y_i)$ We plug in the known values to obtain: $\Delta K.E=6.44\times 10^5+(-3.11\times 10^5)-(1250)(9.81)(16.2)$ $\Delta K.E=1.34\times 10^5J=134KJ$