Question

A ball is having a momentum of $3\mathrm{î}+5\mathrm{ĵ}+\sqrt{15}\mathrm{k̂}$ and is having a mass of $\frac{7}{4}$kg. Determine the kinetic energy of ball.

Answer 1

Let us consider,

1. The relation between momentum and Kinetic energy,
   $\mathrm{K}.\mathrm{E}.=\frac{{\mathrm{p}}^2}{2\mathrm{m}}$
   $\mathrm{p}=$ the momentum of the ball = $3\mathrm{î}+5\mathrm{ĵ}+\sqrt{15}\mathrm{k̂}$ N s
   m = mass of the ball= $\frac{7}{4}$ kg
2. Now, the magnitude of $\mathrm{p}=\left|\mathrm{p}\right|=$ $\sqrt{3^2+5^2+15}$ = $\sqrt{9+25+15}$
   $\sqrt{49}$ $=7$
   $\mathrm{p}2=7*7=49$
   therefore K.E.= $\frac{49}{2*\left({\displaystyle \raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\right)}=49*\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$7$}\right.=14\mathrm{J}$

Hence, the Kinetic energy of the ball is given by $14\mathrm{J}$