91Ó°ÊÓ

The rate of change of angular displacement with respect to time, is known as angular velocity. From velocity and radius of the path, find the angular speed of an observer and Cheetah around the circular paths using the corresponding formula for circular motion. From this, find the linear speed by using its relation with angular speed.

The angular velocity is given as-

$\mathbf{Ó\neg }\mathbf{=}\frac{v}{R}$

where, v is velocity, R is radius and $\mathbf{Ó\neg }$is angular frequency.

Speed of the observer is,
$\begin{array}{c}v=114\frac{\text{km}}{\text{h}}\\ =114(\frac{5}{18}\text{ }\text{m}/\text{s})\\ =31.67\text{ }\text{m}/\text{s}.\end{array}$

Since, an observer is abreast of the Cheetah, bothhave the sameangular speed.

The angular speed of an observer and Cheetah around the circular paths is,

$\mathrm{Ó\neg }=\frac{v}{r}$

$\mathrm{Ó\neg }=\frac{31.67\text{ }\text{m/s}}{100\text{″¾}}$

$\mathrm{Ó\neg }=0.32\text{ r²¹»å/s}$

Hence, the angular speed of an observer and Cheetah around the circular paths is.$\mathrm{Ó\neg }=0.32\text{ r²¹»å/s}$

Linear speed of Cheetah along its path is,

$\begin{array}{c}v=R\mathrm{Ó\neg }\\ =92\text{″¾}(0.32\text{ r²¹»å}/\text{s})(\frac{18}{5}\text{km/h})\\ =1.05×{10}^2\text{km/h}\end{array}$

Hence, the linear speed of Cheetah along its paths is$1.05×{10}^2\text{ }\text{km}/\text{h}.$