Respuesta :
We need to convert the revolutions per second into radians per second, and the radius into meters, as following:
[tex]\begin{gathered} 15\frac{rev}{s}\cdot\frac{2\pi rad}{1\text{rev}}\rightarrow30\pi\text{ }\frac{rad}{s} \\ \\ 2.5ft\cdot\frac{0.3048m}{1ft}\rightarrow0.762m \end{gathered}[/tex]Since the velocity is the product between angular speed and the radius, we get that:
[tex]\begin{gathered} V=30\pi\cdot0.762 \\ \Rightarrow V=71.82\frac{m}{s} \end{gathered}[/tex]Now, let's convert that speed into miles per hour:
[tex]71.82\frac{m}{s}\cdot\frac{1\text{mile}}{1609m}\cdot\frac{60s}{1\min}\cdot\frac{60\min }{1h}\Rightarrow160.69mph[/tex]Answer: 160.96 miles per hour
