If the weight of a person on planet A is half of that on Earth. If the person can jump 0.4 on Earth. Find how high he can jump on planet A.

Let acceleration due to the gravity of the Earth and planet A as g₁ and g₂.
Given, ${\mathrm{g}}_2=\frac{1}{2}{\mathrm{g}}_1$
According to the law of conservation of energy, the potential energy of the person on planet A is equal to the potential energy of the person on earth.
⇒${\mathrm{mg}}_1{\mathrm{h}}_1={\mathrm{mg}}_2{\mathrm{h}}_2$
⇒${\mathrm{h}}_2=\frac{{\mathrm{g}}_1{\mathrm{h}}_1}{{\mathrm{g}}_2}$$=\frac{2{\mathrm{g}}_2{\mathrm{h}}_1}{{\mathrm{g}}_2}$ $=2{\mathrm{h}}_1=2\times 0.4 \mathrm{m}$

⇒${\mathrm{h}}_2=0.8 \mathrm{m}$
Therefore, the person can jump 0.8m high on planet A.