Question

A gasoline-driven lawnmower has a blade that extends out 1.5 ft from its center. The tip of the blade is traveling at the speed of sound, which is 1,100 feet/sec. What is the angular velocity of the tip of the blade? Express your answer in revolutions per minute (rpm). Use 3.14 as an approximation for π and round your answer to the nearest rpm.

Answer 1

what do the think the circumference for the blade would be ?

Answer 2

2(3.14)1.5= 9.4

Answer 3

@mathmath333

Answer 4

\(\large \begin{align} \color{black}{circumference =2\pi r \hspace{.33em}\\~\\
C=2\pi 1.5 \hspace{.33em}\\~\\
C=9.42~~feet \hspace{.33em}\\~\\

\normalsize \text{one revolution = circumference one time }\hspace{.33em}\\~\\
1~revolution=9.42~~feet \hspace{.33em}\\~\\
1~feet=\dfrac{1}{9.42}~~revolution \hspace{.33em}\\~\\
angular ~~velocity=1,100 ~~feet/sec \hspace{.33em}\\~\\
=1,100\times \dfrac{1}{9.42}~~revolution /sec \hspace{.33em}\\~\\
=1,100\times \dfrac{1}{9.42}\times 60~~revolution /min \hspace{.33em}\\~\\
=7006~~revolution /min \hspace{.33em}\\~\\
}\end{align}\)