Question

gravitational potential energy's derivation

Answer 1

https://www.wired.com/2012/03/deriving-the-gravitational-potential-energy/
check it bro

Answer 2

$\mathfrak{ Derivation \: of \: Potential \: Energy}$

$\mathsf{Things \: to \: know \: before\: Derivation}$

$\mathsf{\implies Work \: done = Fs = F × height = \: Fh}$

$\mathsf{\implies Work = Energy}$

$\mathsf{\implies Force = mass \: × \: acceleration \: = ma}$

$\sf{\implies Acceleration \:due \:to \:gravity =\: 'g'}$

$\mathsf{\implies Potential \: Energy \: is \: also \: written \: as \: E_p}$

$\mathsf{Derivation}$

$\mathsf{\hookrightarrow E_p = Work done = Fs = Fh }$

$\mathsf{\hookrightarrow E_p \: = \: Fh \: = ma × h }$

$\mathsf{\hookrightarrow E_p\: = \:Fh \: = mg × h }$

$\mathsf{\hookrightarrow E_p\: = \:mgh }$