Relative velocity practice exam question

[izelkay]

Homework Statement

I would like to check my answers for #3 on this practice exam:
http://cyclotron.tamu.edu/dhy/sample_exam1_phys218.pdf

Homework Equations

The Attempt at a Solution

b) v(plane-wind)x = 30cos30
v(plane-wind)y= 30sin30 + 160

c) 8.44° East of North
d) 1.4 hours

Is this correct or wrong?

 

[Simon Bridge]

We get this sort of question a lot.
The core problem is that you don't know how to tell if your answers are correct or not.
You need to figure it out because you are supposedly training to tackle problems where nobody knows the answer: so there is nobody to ask. At best you'll find out that someone else ends up with the same figures as you - bet they could have made the same mistakes.

How do you tell?

One way is to see if the physical ideas match the end result.

The problem has a pilot tasked with traveling due north (from CLL to 76F) - a wopping 176 nanometers (I'm guessing "nm" means "nautical miles" here - should be M, NM, or nmi). Airspeed is 160knots. The 30knot wind comes in from 30deg west of North.

If the aircraft were to point due North, then the wind will tend to blow it east and south. To correct the pilot will want to turn into the wind ... towards the west. Make sense?

 

[izelkay]

Yeah, that's how I approached the problem. (The wind is approaching from East of North though, not West of North). I feel like I did it right, but I just don't know. I'll just have to go to my professor's open office hours, I guess. Thank you for replying.

 

[Simon Bridge]

<rereads> Oh yes - so it is :/ well done spotting the deliberate mistake ... erm.
note: sin(30)=1/2 =0.5, cos(30)=√3/2 ≈0.87

Wind vector components would be:
30sin(30) = 15knots (W)
30cos(30) = 25.98knots (S)