Relative Motion problem... help! (now with scans of what I have done so far!)

[Byrne]

Relative Motion problem... help! (now with scans of what I have done so far!)

I guess I will write the entire question out first, I am current stuck at part (e) and will provide what I believe are correct answers to the previous portions of the question:

The pilot of a small plane leaves "Here" and set course for "There." It is known that the distance from Here to There is 547 km in the direction [East 29.4 North]. The pilot set course without considering the wind. The maximum crusing speed of the plane was known to be 316 km/h. The pilot sets out at the maximum crusing speed. The wind blows anyway! The wind in the entire area was 78.5 km/h in the direction [North 7 West] and constant throughout the entire flight.

Calculate the following:

(a) The time the pilot calculated it would take for the flight.
Distance of flight (574 km) divided by speed of plane (316 km/h) gives us what the pilot calculated for the time of the flight (1.73 h).

(b) The position the pilot expected to be at after 1.23 hours in the air. (Express this using both component notation and magnitude/direction notation.)
I determined the position to be 388.7 km [West 29.4 East].

(c) The actual velocity of the plane relative to the ground including the wind. (Express this using both component notation and magnitude/direction notation.)
I determined the velocity relative to the ground to be 353.4 km/h [East 41.3 North] by solving the triangle using the information previously given.

(d) The actual position of the plane 1.23 hours after starting.
I determined the actual position of the plane to be 434.7 km [East 41.3 North].

(e) This is where I'm currently at! The displacement from the cirrent location of the pilot 1.23 hours after starting to the actual destination. (Resultatnt Displacement = d2 - d1... a vector subtraction!)
Basically what I did was create a triangle by connecting the actual displacement vector (434.7 km [E 41.3 N]) to the actual destination vector (547 km [E 29.4 N]) at their tails because it is vector subtraction. I determined the interior angle to be 11.9 degrees and used the cosine law to solve for the resultant displacement to find it to be 151.1 km, but after checking my results my answers did not seem to make sense. Please help!

(f) The required heading for the pilot to get to the destination from the current location 1.23 hours after starting out. (Inlcude the wind in this calculation!) (Express this using both component notation and magnitude/direction notation.)
Not here yet...

(e) The length of time required for the entire flight.
Not here yet...

Thanks to anyone for their help! It is truly appreciated...

 

[arildno]

Welcome to PF!
To verify numerical answers is extremely tedious and time-consuming.
Do not expect people at PF to do that part of the job.

So, what do we do?
We will check your procedures, and your set-up , and leave the number-crunching to you.
For example: define your quantities symbolically, and we will will help you manipulate the "symbolic" equations you gain correctly.
(That is, let for example $$\vec{v}_{p}$$ denote the plane's velocity)
From what I can discern, you have the right set-up, so I assume you've made a numerical mistake somewhere.

You might try to re-write your attempts symbolically; it will be easier for people to notice your (possible) mistakes then.

 

[Byrne]

It would probably be easier just for me to scan everything I need to show... I'll be right back.

 

[Byrne]

Sorry... I guess I should have resized them, but they are in order and the question is #3...

http://www.ocgn.com/features/games/misc_images/physics1.jpg

http://www.ocgn.com/features/games/misc_images/physics2.jpg

http://www.ocgn.com/features/games/misc_images/physics3.jpg

http://www.ocgn.com/features/games/misc_images/physics4.jpg

 

[Byrne]

Okay, I guess I'll go even a bit further here... in part (e) (see page 4), I solved the unknown side to be 151.1 km... which is what I am trying to determine. However, this side creates a triangle that cannot be possible because the angles do not add up 180 degrees. The three side lengths are 547 km, 434.7 km, and 151.1 km... I must have made a mistake earlier on the question, but can someone at least read part (e) and tell me what figures I should be using (ie... you should be using the number you found in part (c) with the number given in the question)... that would be appreciated. It's really starting to bug me!