Relative Motion in 2D - a plane & wind speed.

[canucklehead]

Homework Statement

A plane attains an airspeed of 620 km/hr. The plane sets out for a destination 1085 km to the north (a 0° course) but discovers that the plane must be headed 20° east of north to fly there directly. The plane arrives in 2.00 h.

What is the wind speed?
What is the direction of the wind?

Homework Equations

Vf = Vi + a*t
x = vi*t + 0.5a*t^2
vf^2 = vi^2 + 2a*x
V in x-dir'n = |Vi|cosΘ
V in y-dir'n = |Vi|sinΘ

The Attempt at a Solution

I found the north component of velocity as 1850km/2.00h = 542.5km/h

But after that I am completely lost.

Then, I think to find the direction of the wind u need inverse-tan of the y-dir'n velocity & x-dir'n velocity of the wind? But I can't do that without getting the first part first.

Please, help. Thx.

 

[Newton V]

by the way 1850km/2.00h = 542.5m/s is not right...
1850km/2.00h = 542.5m/H... you need use hour
then do this 545.5-620=-74.5km/h (wind speed)
the wind must be negative

 

[canucklehead]

by the way 1850km/2.00h = 542.5m/s is not right...
1850km/2.00h = 542.5m/H... you need use hour
then do this 545.5-620=-74.5km/h (wind speed)
the wind must be negative

Ah, yes, that was a typo. I meant to say 542.5km/h. Thx for pointing out my mistake.

Btw, in your calculation of wind speed you subtracted 620km/h from 545.5km/h... It's supposed to be 542.5km/h, right? Then that means wind speed is -77.5km/h??

 

[Newton V]

yeah...sorry i am doing so many problems...

 

[Newton V]

also please consider the type of air plant... because sometime negative diraction wind actually giving the force to air plane...

 

[LowlyPion]

Not so fast there Amelia Earhart.

It's true that the plane had to fly a longer distance, but the wind speed would have been -77 if the pilot had stayed on a totally Northern course. But he didn't.

Draw a picture and along his flight heading he went in the air 1240km, but he ended up only 1085 km due north.

What wind vector would produce that result?

 

[canucklehead]

Ok, so I found his NE distance to be 1154.6km by Pythagoras.
Then: 1154.6km / 2.00h = 577.3km/h (the speed due NE).

Next: 577.3km/h - 620km/h = -42.7km/h as the wind speed... but it's WRONG. What am I doing wrong?

 

[Newton V]

where you get 1154.6?

 

[Newton V]

1850/2=542.5? it is 1085

 

[LowlyPion]

Ok, so I found his NE distance to be 1154.6km by Pythagoras.
Then: 1154.6km / 2.00h = 577.3km/h (the speed due NE).

Next: 577.3km/h - 620km/h = -42.7km/h as the wind speed... but it's WRONG. What am I doing wrong?

For one thing the hippopotamus is 1240 for your distance vector on the N-20-E heading. 2 hours at 620km/h = 1240.

Then during the time of his flight the wind moved the plane to the North axis.

What is that distance?

That distance divided by the 2 hours is your average wind speed in km/h.