Help! Angular Velocity with Linear Velocity for Trigo

[kinuel8091]

A ride at an amusement park consists of two circular rings of swings. At full speed the swings in the inner ring travel on a circular path with a radius of 32 feet and the swings in the outer ring travel on a circular path with a radius of 36 feet. Each swing makes one complete revolution every 3.25 seconds. How much greater, in miles per hour, is the linear speed of the swings in the outer ring than the linear speed of the swings in the inner ring? Round to the nearest tenth.

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Is this right?

 

[DrPhil]

A ride at an amusement park consists of two circular rings of swings. At full speed the swings in the inner ring travel on a circular path with a radius of 32 feet and the swings in the outer ring travel on a circular path with a radius of 36 feet. Each swing makes one complete revolution every 3.25 seconds. How much greater, in miles per hour, is the linear speed of the swings in the outer ring than the linear speed of the swings in the inner ring? Round to the nearest tenth.

View attachment 3053​

Is this right?

There are 5280 ft/mile.
I think you used ft/km. You did a pretty good job ow writing the units - but the one you left out was wrong!

 

[kinuel8091]

There are 5280 ft/mile.
I think you used ft/km. You did a pretty good job ow writing the units - but the one you left out was wrong!

Like this? what should i do with pi? should i multiply it with the answer? or is that the final answer?

 

[DrPhil]

View attachment 3054

Like this? what should i do with pi? should i multiply it with the answer? or is that the final answer?

Generally, if you are writing an "exact" answer you have to leave the symbol \(\displaystyle \pi\) in your answer explicitly. In this case however, you have already used decimal approximations for the fractions, so you should go ahead and multiply by the \(\displaystyle \pi\)-button on your calculator.

Your answers look good to me.