Question

find the missing info, please show work because I dont understand given:15 rev per secradius of 2.5 ftmissing info: velocity in mph

Answer 1

We need to convert the revolutions per second into radians per second, and the radius into meters, as following:

`\begin{gathered} 15(rev)/(s)\cdot\frac{2\pi rad}{1\text{rev}}\rightarrow30\pi\text{ }(rad)/(s) \\ \\ 2.5ft\cdot(0.3048m)/(1ft)\rightarrow0.762m \end{gathered}`

Since the velocity is the product between angular speed and the radius, we get that:

`\begin{gathered} V=30\pi\cdot0.762 \\ \Rightarrow V=71.82(m)/(s) \end{gathered}`

Now, let's convert that speed into miles per hour:

`71.82(m)/(s)\cdot\frac{1\text{mile}}{1609m}\cdot(60s)/(1\min)\cdot(60\min )/(1h)\Rightarrow160.69mph`

Answer: 160.96 miles per hour