Velocity in two motions (X and Y) ?

[vinny380]

Velocity in two motions (X and Y) ??!

Just wondering if anyone could guide me on this question:

1) You are piloting a small plane, and you want to reach an airport 450 kn due south in 3.0 hours. A wind is blowing from the west at 50.0 km/h. What heading and airspeed should you choose to reach your destination?

First, I drew a triangle on the cordinate gird (X and Y axis). I made one of the legs 50.0 km/h, and the other 450 km.
Ax + Bx = Rx
So Rx = 50.0
Ry = 450

R^2= Rx^2 + Ry^2
R^2= 50^2 + 450^2
R= 452.8 km/h

Is this the correct answer? I really don't know because why then would they include a time (3 hrs.) which I didnt even need or use. I am really stuck on this trouble. Also, am I just trying to find velocity? Whats heading?
Thanks!
BTW - my teacher said this was a pretty easy problem, so it should not be too difficult...

 

[Diane_]

The first problem is that you're mixing units. One leg of your triangle is a velocity and another is a displacement. You can't do that.

Think about the problem for a moment. You know the displacement you want and you know the time - that will give you the average velocity. If you assume that your velocity remains constant, then the average velocity will be the same as the instantaneous velocity. This is where the triangle comes in - at what course and speed do you have to fly so that your airspeed velocity (and I suddenly feel like I'm in a Monty Python movie) vector-summed with the wind's velocity will give you the velocity you want.

Does that help?

 

[vinny380]

I understood the first part - but I am still a little confused ...

So V= D/T
V= 450/3
V= 150 km/h <----- Average velocity

What do I do next?

 

[BerryBoy]

Now you have a velocity (150kmh^-1) due south and a wind of 50 kmh^-1 from the west (pointing east). You can use Pythagoras' Theorem to calulate a value for V (assuming that you want to reach you destination in 3 hours)!
Technically you can travel faster than V if you wanted, you'd just get there sooner a different direction would have to be flown.

And the direction of velocity can be calculated with trigonometry.

If you would like a graphical representation, I'd be glad to help.

Regards,
Sam