Question

An aeroplane's velocity is doubled . what happens to its momentum and kinetic energy ?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}, \\ \mathrm{momentum},\mathrm{p}=\mathrm{mv} \\ \mathrm{and}\mathrm{kinetic}\mathrm{energy},\mathrm{KE}=\frac{1}{2}{\mathrm{mv}}^2 \\ \mathrm{If}\mathrm{velocity}\mathrm{is}\mathrm{doubled},\mathrm{then} \\ \mathrm{p}\text{'}=\mathrm{m}\left(2\mathrm{v}\right) \\ \mathrm{p}\text{'}=2\mathrm{mv}=2\mathrm{p} \\ \mathrm{and} \\ \mathrm{KE}\text{'}=\frac{1}{2}\mathrm{m}{\left(2\mathrm{v}\right)}^2 \\ \mathrm{KE}\text{'}=4\times \frac{1}{2}{\mathrm{mv}}^2 \\ \mathrm{KE}\text{'}=4\mathrm{KE} \end{gathered}$$