Answer:
191.59 mile/hour is the linear speed of the tip of a lawnmower blade.
Step-by-step explanation:
[tex]v=r\times \omega [/tex]
v = linear speed
r = radius of circular path
[tex]\omega [/tex] = Angular speed
We have:
Revolution of blade in a minute = 2300
1 hour = 60 min
Revolution in 1 hour or 60 min = 2300 × 60 =138000 revolution per hour
Angular speed of blade =
[tex]\omega =138000 \times 2\pi=867,079.57 rad/hour[/tex]
Width or diameter of the blade = d = 28 cm
Radius of blade = [tex]\frac{28 inch}{2}=14 inch[/tex]
1 mile = 63360 inch
[tex]14 inch=\frac{14}{63360} mile[/tex]
Linear speed of the blade: v
[tex]v=867,079.57 rad/hour\times \frac{14}{63360} mile=191.59 mile/hour[/tex]
191.59 mile/hour is the linear speed of the tip of a lawnmower blade.
