Who wants a medal?!
A waterwheel has a radius of 1 foot, and a water bug has attached itself to the wheel at water level as shown in the diagram below.
(will include link of the diagram)

As the wheel rotates counterclockwise, setting the boat in motion, the water bug will travel along the wheel. The boat travels at a rate of 1 foot per second. How many times did the water bug go beneath the water level if the boat traveled a distance of 109 feet?

Question

Who wants a medal?!
A waterwheel has a radius of 1 foot, and a water bug has attached itself to the wheel at water level as shown in the diagram below.
(will include link of the diagram)

As the wheel rotates counterclockwise, setting the boat in motion, the water bug will travel along the wheel. The boat travels at a rate of 1 foot per second. How many times did the water bug go beneath the water level if the boat traveled a distance of 109 feet?

anonymous · Answer

A. 17
B. 34
C. 54
D. 75

amriju · Answer

34

anonymous · Answer

Can you tell me how you got that answer?

amriju · Answer

its 17 actually..it is a case of pure rolling...u know pure rolling?

anonymous · Answer

Never heard of it.
I'm currently in the topic "Graphing Sine and Cosine" if that is of any help.

amriju · Answer

this question is part of dynamics...we call it pure rolling in mechanics

anonymous · Answer

Is there a formula you use?

amriju · Answer

yes v=r.w...v=translational velocity, w= angular velocity and r = radius

anonymous · Answer

So with this problem
r = 1 ft
but how do you get v and w?

amriju · Answer

the speed of the boat is the translational velocity of the wheel

anonymous · Answer

so 1 ft per second?

amriju · Answer

yup

amriju · Answer

so do u know angular velocity?

anonymous · Answer

Do you need to solver for the degree/radian of the angle to find it?

anonymous · Answer

*solve

amriju · Answer

yup..u need radians and stuff..once you have determined the angular velocity...( thats the angle traversed by a rotating stuff..)..u can see that in a whole 2pi radian rotation..the bug is dipped once..now find the time to rotate by 2 pi radians...in that specific time the bug is dipped once..now see the time the boat traverses..its 109 secs..( coz the speed is 1 ft/ sec..and distance 109 ft)...so find the number of times the bug is dipped..its 17.3...flooor it...17

amriju · Answer

are you somewhat clear?

anonymous · Answer

Could you show me how to plug that into the formula you gave me?
r=v w
1ft= 109s (2pi)     or is that wrong?

amriju · Answer

v=rw..v= 1ft/sec, r=1 ft=>w= 1 rad/sec..read any mechanics book..about rolling

anonymous · Answer

Are you in high school or college? (if you're uncomfortable answering that question, I understand.)

amriju · Answer

college..

anonymous · Answer

Yeah that makes sense.

anonymous · Answer

Thank you for your help! :)

amriju · Answer

wc.:)