A space research pod goes around the earths circumference in 2 hours. Find it’s angular velocity in radians per second and it’s linear speed in feet per minute and in miles per hour.

Respuesta :

Let's find the angular velocity:

[tex]\begin{gathered} \omega=2\pi f \\ f=\frac{1}{T} \\ \omega=\frac{2\pi}{T} \\ \omega=\frac{2\pi}{2}=\frac{\pi rad}{h} \end{gathered}[/tex]

We need to find the velocity in radians per second, so:

[tex]\pi\frac{rad}{h}\times\frac{1h}{3600s}=\frac{\pi}{3600}\approx\frac{0.0008727rad}{s}[/tex]

Let's find the linear speed:

[tex]v=\omega\cdot r[/tex]

[tex]v=\omega\cdot(6371\operatorname{km})=\frac{5559.74632m}{s}[/tex]

We need to express this speed in feet per minute, so:

[tex]5559.746332\frac{m}{s}\times\frac{3,28084ft}{1m}\times\frac{60s}{1\min}=\frac{1094438.289ft}{\min }[/tex]

Now in miles per hour:

[tex]1094438.289\frac{ft}{\min}\times\frac{1mi}{5280ft}\times\frac{60\min }{1h}=\frac{12436.79874mi}{h}[/tex]