# Help with an airplane problem (relative velocity)

#### ccsmarty

1. Homework Statement

An airplane pilot sets a compass course due west and maintains an airspeed of 218 km/hr. After flying for a time of 0.510 hr, she finds herself over a town a distance 124km west and a distance 16 km south of her starting point. Find the magnitude of the wind velocity (in m/s).

2. Homework Equations

3. The Attempt at a Solution 1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

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#### learningphysics

Homework Helper
You're making the assumption that wind velocity is southbound... it might not be...

#### ccsmarty

What would be a better assumption then? I could use any help because I've been working on this problem for a while, and I'm not getting anywhere :(.

#### PhanthomJay

Homework Helper
Gold Member
What would be a better assumption then? I could use any help because I've been working on this problem for a while, and I'm not getting anywhere :(.
You should calculate the plane's velocity with respect to earth (ground speed) first. (I'm no pilot, but i would have thought that if she set her compass west, she'd end up due west, but i guess not, according to the problem).

#### rootX

Try solving other way, so that you can avoid geometry.

like

v[ab]= v[ar]+v[rc]+........+v[pq]+v[qb]
and v[xy] = -v[xy]

#### learningphysics

Homework Helper
What would be a better assumption then? I could use any help because I've been working on this problem for a while, and I'm not getting anywhere :(.
You know the wind has a component southbound... because the plane ends up south... you don't know whether it has a east bound or west bound component...

I like rootx's method... divide wind into 2 components... vsouth, and vwest (ie assume wind is southwest, if vwest comes out negative then it was pointed southeast).

You can easily calculate the southbound component... you know the southbound displacement...

For the westbound component you need to add the plane's velocity...

#### FedEx

You know the wind has a component southbound... because the plane ends up south... you don't know whether it has a east bound or west bound component...

I like rootx's method... divide wind into 2 components... vsouth, and vwest (ie assume wind is southwest, if vwest comes out negative then it was pointed southeast).

You can easily calculate the southbound component... you know the southbound displacement...

For the westbound component you need to add the plane's velocity...
We can solve it by vectors. Learning physics has made a good point that the wind's velocity can be in any direction so in that case we can resolve the vector and proceed.

But suppose that the wind is not even southwest or southeast but it is some other add angle like say 65 or 35. Is this case possible/ I think it is . So in this case what to do? Hence i feel that the wind's direction is only in the south. And then we can do it by the normal equations.

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#### learningphysics

Homework Helper
But the plane ends up south... so the wind must have a southbound component, not northbound...

Also, 0.51h * 218km/h = 111.18 km, so the plane alone would only go 111.18km in 0.51 hrs... But the total westbound displacement is 124km as given in the problem... so the wind has a westbound component.

They gave the time it took... I agree that if we didn't have the time, we'd have to assume wind direction... but since the time is given we don't need to.

#### PhanthomJay

Homework Helper
Gold Member
I never was too fond of the law of cosines, but it certainly seems applicable here, where the plane's air velocity is given, and it's ground velocity, and angle between each, is easily calculated from the given data...

#### FedEx

But the plane ends up south... so the wind must have a southbound component, not northbound...

Also, 0.51h * 218km/h = 111.18 km, so the plane alone would only go 111.18km in 0.51 hrs... But the total westbound displacement is 124km as given in the problem... so the wind has a westbound component.

They gave the time it took... I agree that if we didn't have the time, we'd have to assume wind direction... but since the time is given we don't need to.
Yes, you are right. I totally forgot that the time was given.