Question #b625e

1 Answer
Jan 1, 2017

Answer:

#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.