What is the wind velocity in km/h and what angle it it north of east?

[physicsss]

A light plane is headed due south with a speed relative to still air of 200 km/h. After 1 hour, the pilot notices that they have covered only 190 km and their direction is not south but southeast. What is the wind velocity in km/h and what angle it it north of east?

 

[Tide]

The velocity of the wind is the difference between the actual velocity of the plane and the "intended" velocity of the plane.

 

[physicsss]

...

not really...in the book the intended is 240 km/h but the actual is 180 km and the answer they give is 170 k/h with an angle of 41.5 N of E.

 

[Tide]

not really...in the book the intended is 240 km/h but the actual is 180 km and the answer they give is 170 k/h with an angle of 41.5 N of E.

Remember, velocity is a vector!

 

[physicsss]

but there's no angles given.

 

[Tide]

Due south and southeast sound like angles to me! :-)

 

[physicsss]

i still don't get it. angle is 45 degrees?

 

[Tide]

LaTex doesn't seem to be working so I'll try this:

The actual speed of the plane is 190/sqrt(2) km/h so it's actual velocity is (1, -1)*190/sqrt(2).

The "intended velocity of the plane is (0, -1)*200 km/h.

The difference between them is the wind velocity:
(190/sqrt(2), 200 - 190/sqrt(2))

Now just divide the y component by the x component to find the tangent of the angle you're looking for.

A drawing might help you see it better.

 

[HallsofIvy]

A drawing might help you see it better.

That should be the first thing you do!

 

[physicsss]

Tide, Does Latex work now? I still don't get the answers that the book got using what you did...