Question

Question #b625e

Answer 1

`56.23` mph, rounded to two decimal places.

Explanation:

For circular motion we have the following equation connecting linear velocity `v`, of a point located at radius `r`, and rotating with an angular frequency `omega`

`v=romega` ........(1)
and `omega=2pif` .....(2)
where `f` is frequency of rotation.

Combining (1) and (2) we get
`v=r(2pif)`
Inserting given values after converting inch to mile and minute to hour

1. For `14`​-inch diameter blade: `r=14/2=7` inch
   `v_14=(7/(12xx3xx1760))(2pixx3150/(1/60))`
   `=>v_14=7xx(2pixx3150xx60)/(12xx3xx1760)`
   `=131.20` mph
2. Similarly for `8`​-inch diameter blade: `r=8/2=4` inch
   `=>v_8=4xx(2pixx3150xx60)/(12xx3xx1760)`
   `=74.97` mph

Difference in linear velocity of two`=v_14-v_8`
`=131.20-74.97`
`=56.23` mph, rounded to two decimal places.