An aircraft is flying at the speed of 354km/hr relative to the air is observed from the ground to have a velocity of 300km/hr in the north east direction. The wind is blowing from east. Find the speed of the wind and the direction to which the aircraft is heading.

To find the speed of the wind and the direction to which the aircraft is heading, we need to break down the velocity of the aircraft into its components: one in the direction of the wind (east-west component) and the other perpendicular to the wind (north-south component).

Let's define:
- Vw as the speed of the wind
- θ as the angle between the aircraft's direction and the north direction (clockwise)

Given:
- Velocity of the aircraft relative to the air = 354 km/hr
- Velocity of the aircraft observed from the ground in the north-east direction = 300 km/hr

To find the wind speed (Vw), we can use the Pythagorean theorem:

Vw^2 = (Velocity observed from the ground)^2 - (Velocity relative to the air)^2

Plugging in the known values:
Vw^2 = (300 km/hr)^2 - (354 km/hr)^2

Now, let's solve for Vw:

Vw^2 = 90000 km^2/hr^2 - 125316 km^2/hr^2
Vw^2 = -35316 km^2/hr^2

Since a square value can't be negative, something is wrong. We made an error in setting up the equations.

Let's try a different approach.

The observed velocity of the aircraft can be decomposed into north (Vn) and east (Ve) components:

Vobserved_north = Vn = 300 km/hr
Vobserved_east = Ve = 300 km/hr

The relative velocity of the aircraft (velocity with respect to the air) can also be decomposed into north (Vn') and east (Ve') components:

Vrelative_north = Vn' = Vwind_north + Va_north = Vwind_north + Vair_north
Vrelative_east = Ve' = Vwind_east + Va_east = Vwind_east + Vair_east

Since the wind is blowing only from the east, we can assume that Vwind_north = 0.

Now, let's express Vrelative_north and Vrelative_east in terms of Vn, Ve, and Vw:

Vrelative_north = Vwind_north + Vair_north = 0 + Vair_north = Vair_north

Vrelative_east = Vwind_east + Vair_east = Vwind_east + 0 = Vwind_east

Since the aircraft is flying with a speed of 354 km/hr relative to the air, we have:

Vair_north = Vn' = 354 km/hr
Vair_east = Ve' = 0 (since there is no wind blowing from the north)

From Vrelative_north = Vair_north, we get:

Vwind_north = Vair_north = 354 km/hr

From Vrelative_east = Vwind_east, we get:

Vwind_east = Vobserved_east - Ve = 300 km/hr - Ve

Now we have two equations:

Vwind_north = 354 km/hr
Vwind_east = 300 km/hr - Ve

Solving these equations simultaneously, we can find both Vwind and Ve.

We can see that Vwind_north is 354 km/hr, indicating that the wind is blowing from the north with a speed of 354 km/hr.

To find Vwind_east, we can substitute the value of Vwind_north into the second equation:

Vwind_east = 300 km/hr - Ve

Since we don't have the exact value of Ve, we can't determine the exact value of Vwind_east or the direction to which the aircraft is heading. We need additional information to calculate that.