Answer:
[tex]\large\text{$25.412$hrs}[/tex]
Explanation:
[tex]\large\text{We will use the formula to calculate the time period of the }[/tex]
[tex]\large\text{satellite:$}[/tex]
[tex]\large\text{$T=\dfrac{2\pi r}{v}$}[/tex]
[tex]\large\text{where,$}[/tex]
[tex]\large\text{$r = $ orbital radius (distance from center of earth to the satellite)}[/tex]
[tex]\large\text{$v=$ velocity of satellite}[/tex]
[tex]\large\text{First let's calculate the value of $r.$}[/tex]
[tex]\large\text{$r=$ Radius of earth + height of satellite}[/tex]
[tex]\large\text{$=6400$km + 30000km}[/tex]
[tex]\large\text{$=$ 36400km}[/tex]
[tex]\large\text{$= $ 36400000m}[/tex]
[tex]\large\text{$=3.64\times10^7$m}[/tex]
[tex]\large\text{Convert velocity into m/s:$}[/tex]
[tex]\large\text{$v= $ 2.5km/s = $2.5\times10^3$m/s}[/tex]
[tex]\large\text{Calculate the time period:$}[/tex]
[tex]\large\text{$T=\dfrac{2\pi(3.64\times10^7)}{2.5\times10^3}$}[/tex]
[tex]\large\text{$=91.48\times10^3$s}[/tex]
[tex]\large\text{$=\dfrac{91.48\times10^3}{3600}$hrs}[/tex]
[tex]\large\text{$\approx 25.412$hrs}[/tex]
