Calculating Arc Length for a Circling Airplane

[DethRose]

Hey been working on this problem for an hour.

An airplane circles the airport control tower 1.0 times while 4.5 km away. Calculate the length of arc through which the plane travels.

The only formula i can think of that remotely resembles something to be use on this is F=mv^2/r

please help have an exam today haha


thanks a lot

 

[mjfairch]

Well, the arc-length of 1 revolution around a circle is simply the circumference of that circle. However, in this problem, I'm not sure how you know the circle's radius, since it doesn't tell you at what altitude the plane is when it begins circling. For example, if it was directly 4.5km overhead, then the radius would be 0 (an extreme case), or if it was somewhere in between, it's radius would obviously increase accordingly. Were you not given the altitude?

 

[DethRose]

nope...thats the exact question i was given

 

[Parth Dave]

Umm, I think you are to assume that the radius is 4.5 km, and that the plane is 4.5 km away is not referring to altitude at all. If this isn't the case then you can't solve it, as mjfairch eluded to. Another quick suggestion, don't spend an hour on a question. It does you no good. On a test, you aren't given an hour to solve problems. So i suggest, just get help after about 15 mins. You're really not helping yourself by spending so much time on questions.

 

[mjfairch]

Were you given a picture or the angle of inclination from the tower to the plane? Do you see my point, or am I misreading the problem somehow?

For example, suppose the origin of a right-handed coordinate system is where the ground meets the tower, and the angle up from the ground to the tower was 45 degrees. Then, using basic trig, the radius of its circle would be $r=4.5\cos(45^\circ)=3.18$km. Of course, its circumference is then $C=2\pi r=20.0$km. If the inclination were $30^\circ$, however, then we'd have $C=24.5$km using the same math.

Without an altitude or angle of inclination, you might assume 4.5km is the radius as Parth Dave suggests. Else, the problem results in a 1-parameter family of solutions (with the altitude or angle being the parameter).

 

[DethRose]

nope that's all i was given

 

[FulhamFan3]

you guys think way too hard.

2*pi*R

R=4.5km

 

[fizixx]

fulham:

exactly.