Question

A baseball of mass$\mathbf{144}\mathbf{}\mathit{g}$has a velocity of$\mathbf{(}\mathbf{22}\mathbf{,}\mathbf{23}\mathbf{,}\mathbf{-}\mathbf{11}\mathbf{)}$. What is the kinetic energy of the baseball?

Short answer

The kinetic energy of the baseball is,$81.65J$.

Step-by-step solution

Identification of the given data 

The given data can be listed below as,

- The mass of baseball is, $m=144\mathrm{g}=144\times {10}^3\mathrm{kg}$

- The speed of baseball is, $v=(22,23,-11)\mathrm{m}/\mathrm{s}$

Significance of kinetic energy

The kinetic energy is a form of energy that an object or particle retains due to its motion.

Determination of the kinetic energy in +x direction

The relation of kinetic energy is expressed as,

$K-\frac{1}{2}m{v}^2$

(i)

Here $K$is the kinetic energy, $m$is the mass of the baseball and $V$is the speed of the baseball.

The speed of the baseball is expressed as,

$V=(22\hat{i}+23\hat{j}-11\hat{k})\mathrm{m}/\mathrm{s}$

$\stackrel{\mathrm{L}}{\mathrm{v}}\mid =\sqrt{{22}^2+{23}^2+(-11{)}^2}\mathrm{m}/\mathrm{s}$

$=33.67m/s$

Substitute $144\times {10}^{-3}\mathrm{kg}$for $m$and $33.67\mathrm{m}/\mathrm{s}$for $v$in the equation (i).

$K=\frac{1}{2}\times 144\times {10}^{-3}\mathrm{kg}\times (33.67\mathrm{m}/\mathrm{s}{)}^2$

$=81.65J$

Hence the kinetic energy of the baseball is, localid="1657723057055" $81.65J$.