# In what direction should the plane head?

Question:

An airplane, whose air speed is 600km/h is supposed to flyy in a straight path 35 degrees north of east. But a steady 100 km/h wind is blowing from the north. In what direction should the plane head?

Here is an answer by someone(is it right?)

Vp (vector velocity of the plane) = 600cos35i + 600sin35j

Vw (vector velocity of the wind) = -100j

The direction in which it shud go is the direction of the velocity of the plane relative to the wind, Vpw

As a rule Vpw= Vp - Vw

=> Vpw= 491.5i + 344.1j + 100j
= 491.5i + 444.1j

|Vpw|= 662.4 km/h (speed at which the plane heads, direction is given by tanA=j/i=444.1/491.5)

tanA = 444.1/491.5
A = 42 degrees.

I don't see anything wrong with "someone's" reasoning, and I got the same answer when I did the problem, if it reassures you.

nrqed
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Saketh said:
I don't see anything wrong with "someone's" reasoning, and I got the same answer when I did the problem, if it reassures you.
I am not convinced the calculation shown by the OP is correct.
How do you define "air speed" of the plane? *My* interpretation is that it's the speed of the plane relative to (still) air. But the OP uses this as being the speed of the plane relative to the ground. This does not make sense to me. So I diagree that this is the correct calculation.

Patrick

bye

is nrqed online again?

nrqed
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borisleprof said:
is nrqed online again?
On and off.

So you take the "600 km/hr air speed" to be the speed relative to the ground? Maybe. But to me, saying that an airplane flies at a speed of X km/hr means the speed relative to the air. It's like the speed of a boat. Who knows what the speed relative to th eground will be, it all depends on the speed of the river flowing.

So it all amounts to a question of interpretation. In this problem, does the 600 km/hr represent a technical specification of the plane (in which case it would have to be measured relative to air)? Or is it supposed to mean "in that particular situation, with the wind blowing at that speed and in that direction, one observes the plane moving at a speed of 600 km/hr as seen from the ground in which case the solution proposed by the OP is correct.

I personally believe that the interpretation is the first one but I won't argue about it.

Regards

Patrick