iohanetc

2021-02-18

A gondola on an amusement park ride, similar to the Spin Cycle at Silverwood Theme Park, spins at a speed of 13 revolutions per minute. If the gondola is 25 feet from the ride's center, what is the linear speed of the gondola in miles per hour?

cheekabooy

Skilled2021-02-19Added 83 answers

The relationship of the linear speed vv to the angular speed ω (in radians per unit time) and radius r is:

$v=\omega r$

Convert the angular speed to radians per hour:

$\omega =\left(13re\frac{v}{min}\right)\cdot \left(2\pi ra\frac{d}{1}rev\right)\cdot \left(60\frac{min}{1}hr\right)=1560\pi ra\frac{d}{h}r$

Convert the radius to miles:

$r=25ft\cdot \left(1m\frac{i}{5280}ft\right)=\frac{25}{5280}mi\le s$

So, the linear speet is:

$v=1560\pi ra\frac{d}{h}r\cdot \left(\frac{25}{5280}\right)mi\le s$

$v\approx 23.2m\frac{i}{h}r$

Convert the angular speed to radians per hour:

Convert the radius to miles:

So, the linear speet is:

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