Gravitational potential and potential energy

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Question

A person brings a mass of $2 k g$ from A to B . The increase in kinetic energy of the mass is 4 and the work done by the person on the mass is $- 10 J$ , then $V_{A} - V_{B} =$ _______ Where $V_{A}$ and $V_{B}$ are gravitational potentials at A and B.

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Solution

$W_{A \to B} + W_{P e r s o n} = 4$
$\begin{matrix} W_{A B} - 10 = 4 \\ W_{A B} = 14 J \end{matrix}$ $m [V_{A} - V_{B}] = 14$

$\begin{matrix} 2 [V_{A} - V_{B}] = 14 \\ ∴ V_{A} - V_{B} = 7 j o u l e / k g \end{matrix}$

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