Gravitational Potential Energy v_1

`v_1 = sqrt( v_2 ^2+2g y_2 -2g y_1 -(2 W_(other) )/ m )`

`(y_1)"Initial Position"`

`(y_2)"Final Position"`

`(W_(other))"Work by Other Force"`

`(m)"Mass"`

`(v_2)"Final Velocity"`

University Physics 12th Edition, Chapter 7, Equation #7.8