| Topic: |
Science > Physics |
| User: |
"noclevername" |
| Date: |
11 Feb 2005 11:35:54 AM |
| Object: |
Need help with vector problem |
Hi all. I am new to this forum but I am somewhat of a forum junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for the
book we use and so far the book publishers contend their answer is
correct. I, however, cannot get either the instructor's answer nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
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| User: "John Popelish" |
|
| Title: Re: Need help with vector problem |
11 Feb 2005 12:12:23 PM |
|
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noclevername wrote:
Hi all. I am new to this forum but I am somewhat of a forum junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for the
book we use and so far the book publishers contend their answer is
correct. I, however, cannot get either the instructor's answer nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
Assuming that your description means that the wind is out of the
NorthEast at 80 km/hr (I don't know what the 45 degrees refers to,
unless this is a redundant reference ot the direction), I think the
problem involves having the east west component of the wind canceled
by an equal but opposite east west component of the planes velocity.
The wind has an out of the East velocity component of
sin(45)*80km/hr=56.6 km/hr.
So the plane must be angled toward the East so that the sine of that
angle times its forward velocity is the same speed.
56.6km/hr=sin(a)*250km/hr.
I solve that equations for a=13 degrees.
That angle leaves a Northerly component of air speed of
250km/hr*cos(13)=243.5km/hr.
But there is still the northerly component of the wind or
cos(45)*80km/hr=56.6km/hr that is effective head wind for the plane,
so the ground speed of the plane is 243.5-56.6=186.9km/hr.
Does this correspond to either the book's or the teacher's answer?
--
John Popelish
.
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| User: "Michael J. Strickland" |
|
| Title: Re: Need help with vector problem |
11 Feb 2005 12:50:20 PM |
|
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"John Popelish" <jpopelish@rica.net> wrote in message
news:420CF587.38FE7631@rica.net...
noclevername wrote:
Hi all. I am new to this forum but I am somewhat of a forum junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for the
book we use and so far the book publishers contend their answer is
correct. I, however, cannot get either the instructor's answer nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
Assuming that your description means that the wind is out of the
NorthEast at 80 km/hr (I don't know what the 45 degrees refers to,
unless this is a redundant reference ot the direction), I think the
problem involves having the east west component of the wind canceled
by an equal but opposite east west component of the planes velocity.
The wind has an out of the East velocity component of
sin(45)*80km/hr=56.6 km/hr.
So the plane must be angled toward the East so that the sine of that
angle times its forward velocity is the same speed.
56.6km/hr=sin(a)*250km/hr.
I solve that equations for a=13 degrees.
That angle leaves a Northerly component of air speed of
250km/hr*cos(13)=243.5km/hr.
I also get a required course of 13 deg west of north (Bearing 347 deg).
But there is still the northerly component of the wind or
cos(45)*80km/hr=56.6km/hr that is effective head wind for the plane,
I think you mean tailwind. (wind that blows NorthEast ).
In aeronautics, wind directions specify the direction the wind blows.
so the ground speed of the plane is 243.5-56.6=186.9km/hr.
I get a ground speed of: 243.5 + 56.6 = 300 km/hr northward.
....
--
---------------------------------------------------------------
Michael J. Strickland
Quality Services
703-560-7380
---------------------------------------------------------------
.
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| User: "John Popelish" |
|
| Title: Re: Need help with vector problem |
11 Feb 2005 01:14:39 PM |
|
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"Michael J. Strickland" wrote:
"John Popelish" <jpopelish@rica.net> wrote in message
news:420CF587.38FE7631@rica.net...
noclevername wrote:
Hi all. I am new to this forum but I am somewhat of a forum junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for the
book we use and so far the book publishers contend their answer is
correct. I, however, cannot get either the instructor's answer nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
Assuming that your description means that the wind is out of the
NorthEast at 80 km/hr (I don't know what the 45 degrees refers to,
unless this is a redundant reference ot the direction), I think the
problem involves having the east west component of the wind canceled
by an equal but opposite east west component of the planes velocity.
The wind has an out of the East velocity component of
sin(45)*80km/hr=56.6 km/hr.
So the plane must be angled toward the East so that the sine of that
angle times its forward velocity is the same speed.
56.6km/hr=sin(a)*250km/hr.
I solve that equations for a=13 degrees.
That angle leaves a Northerly component of air speed of
250km/hr*cos(13)=243.5km/hr.
I also get a required course of 13 deg west of north (Bearing 347 deg).
But there is still the northerly component of the wind or
cos(45)*80km/hr=56.6km/hr that is effective head wind for the plane,
I think you mean tailwind. (wind that blows NorthEast ).
In aeronautics, wind directions specify the direction the wind blows.
so the ground speed of the plane is 243.5-56.6=186.9km/hr.
I get a ground speed of: 243.5 + 56.6 = 300 km/hr northward.
That is why I stated my assumptions up front. In weather forecasting,
wind direction refers to the direction it comes from.
--
John Popelish
.
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| User: "Philip Holman" |
|
| Title: Re: Need help with vector problem |
11 Feb 2005 05:18:01 PM |
|
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"John Popelish" <jpopelish@rica.net> wrote in message
news:420D041F.E62CA6CF@rica.net...
"Michael J. Strickland" wrote:
"John Popelish" <jpopelish@rica.net> wrote in message
news:420CF587.38FE7631@rica.net...
noclevername wrote:
Hi all. I am new to this forum but I am somewhat of a forum
junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am
having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for
the
book we use and so far the book publishers contend their answer
is
correct. I, however, cannot get either the instructor's answer
nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at
a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due
North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
Assuming that your description means that the wind is out of the
NorthEast at 80 km/hr (I don't know what the 45 degrees refers to,
unless this is a redundant reference ot the direction), I think the
problem involves having the east west component of the wind
canceled
by an equal but opposite east west component of the planes
velocity.
The wind has an out of the East velocity component of
sin(45)*80km/hr=56.6 km/hr.
So the plane must be angled toward the East so that the sine of
that
angle times its forward velocity is the same speed.
56.6km/hr=sin(a)*250km/hr.
I solve that equations for a=13 degrees.
That angle leaves a Northerly component of air speed of
250km/hr*cos(13)=243.5km/hr.
I also get a required course of 13 deg west of north (Bearing 347
deg).
But there is still the northerly component of the wind or
cos(45)*80km/hr=56.6km/hr that is effective head wind for the
plane,
I think you mean tailwind. (wind that blows NorthEast ).
In aeronautics, wind directions specify the direction the wind blows.
so the ground speed of the plane is 243.5-56.6=186.9km/hr.
I get a ground speed of: 243.5 + 56.6 = 300 km/hr northward.
That is why I stated my assumptions up front. In weather forecasting,
wind direction refers to the direction it comes from.
Is the wind that blows NE, a NE wind? I would take this to mean it's a
SW wind. But, stating you assumption makes it crystal clear what
conditions you are using. If the OP would post the answer in the book,
we could at least identify the intent.
Phil H
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| User: "tadchem" |
|
| Title: Re: Need help with vector problem |
11 Feb 2005 11:47:33 AM |
|
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noclevername wrote:
Hi all. I am new to this forum but I am somewhat of a forum junkie
elsewhere.
Anyway, I am currently taking calculas based physics and am having a
lot of trouble with one particular problem, (as are others in my
class). The professor's answer and the answer in the back of the
book also differ. I checked the latest corrected solutions for the
book we use and so far the book publishers contend their answer is
correct. I, however, cannot get either the instructor's answer nor
the back of the book answer so I am hoping someone can help me.
Thanks in advanced for your help. Here is the problem:
A plane flies 250km/hr. There is a wind that blows NorthEast at a
45degree angle at 80km/hr.
a- what angle and direction should the plane fly to head due North?
b- what is the plane's airspeed relative to the ground?
Again, thanks in advanced for any help you can give me.
I won't do your homework for you.
I will tell you *how* to solve the problem.
Step 1:
Draw a diagram. You have 3 vectors to combine into a triangle. One
(the windage) is length 80 (km/hr) and angle 45=B0 from the vertical.
The second one (net velocity) is due north (angle 0=B0) and *equals the
sum of the other two*.
The third (airspeed) is length 250 (km/hr) and starts at the same point
as the second.
The first will start at the *endpoint* of the third and end at the
*endpoint* of the second.
Roughly:
A
/|
/ |
/ |
/ |
B |
\ |
\ |
\ |
\|
C
The first is BA, the second is CA, and the third is CB.
Step 2: Apply some trigonometry. You know the lengths CB and BA, and
the angle A. Calculate the rest. Sometimes you may get ambiguous
results, so use a little common sense to decide which of the two
answers your quadratics give you is reasonable for this problem.
OK. You're stumped. Have you forgotten the Law of Sines?
Tom Davidson
Richmond, VA
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