Question

A gondola on an amusement park ride spins at a speed of 13revolutions per minute. If the gondola is 28 feet from the​ ride's center, what is the linear speed of the gondola in miles per​ hour?

Answer 1

`3.81" miles/hour"`

Explanation:

The circumference of the circle is:

`C = 2pi(28" ft")`

`C = 56pi" ft"`

Begin dimensional analysis by writing this over 1:

`(56pi" ft")/1`

The gondola travels the circumference 13 times per minute:

`(56pi" ft")/1(13)/(1" min")`

Please observe that we have obtained a speed with the units of ft/min.

Convert feet to miles:

`(56pi" ft")/1(13)/(1" min")(1" mile")/(5280" ft")`

Please observe that the feet units cancel and the speed is now in units of miles/min:

`(56picancel(" ft"))/1(13)/(1" min")(1" mile")/(5280cancel(" ft"))`

Convert minutes to hour by multiplying by `(60" min")/(1" hour")`:

`(56picancel(" ft"))/1(13)/(1" min")(1" mile")/(5280cancel(" ft"))(60" min")/(1" hour")`

Please observe that the minutes units cancel and we are left with a speed in the units of miles/hour:

`(56picancel(" ft"))/1(13)/(1cancel(" min"))(1" mile")/(5280cancel(" ft"))(60cancel(" min"))/(1" hour")`

Multiply and divide the factors:

`3.81" miles/hour"`