The mass of the moon is (1)/(144) times the mass of a planet and...

As we know, escape velocity is given by, ${v}_{escape} = \sqrt{\dfrac{2GM}{R}}$

Now, ${v}_{planet} = \sqrt{\dfrac{2GM}{R}} = v$

${v}_{Moon} = \sqrt{\dfrac{2GM \times 16}{144 \times R}} = \dfrac{1}{3}\sqrt{\dfrac{2GM}{R}} = \dfrac{v}{3}$