To find the velocity of the aircraft with respect to the ground, we can use vector addition. The velocity of the aircraft is the sum of its own velocity (due North) and the velocity of the wind.
Let's break down the velocities into their components:
Velocity of the aircraft (due North): 150 km/hr (North)
Velocity of the wind (from the North-West): 60 km/hr (North-West)
Now, we can find the resultant velocity by adding the corresponding components:
North Component: Velocity of the aircraft (150 km/hr) West Component: Velocity of the wind (60 km/hr)
Using the Pythagorean theorem, we can calculate the magnitude of the resultant velocity:
Resultant Velocity = √(North Component^2 + West Component^2)
Resultant Velocity = √(150^2 + 60^2)
Resultant Velocity ≈ √(22500 + 3600)
Resultant Velocity ≈ √26100
Resultant Velocity ≈ 161.24 km/hr (rounded to two decimal places)
To find the direction of the resultant velocity, we can use trigonometry. We can calculate the angle using the inverse tangent:
Angle = atan(West Component / North Component)
Angle = atan(60 km/hr / 150 km/hr)
Angle ≈ atan(0.4)
Angle ≈ 21.80 degrees (rounded to two decimal places)
Therefore, the velocity of the aircraft with respect to the ground is approximately 161.24 km/hr in the direction of 21.80 degrees east of north.