A helicopter pilot is on a heading of [180 degrees] with an airspeed of 125 km/h. If there is a 50 km/h wind blowing from the east, what is the velocity of the plane relative to the ground?
To find the velocity of the helicopter relative to the ground, we need to consider the effect of both the helicopter's airspeed and the wind.
First, let's break down the helicopter's velocity into its components. We have:
- Helicopter airspeed: 125 km/h
- Heading of the helicopter: 180 degrees
Now, let's consider the wind's velocity:
- Wind speed: 50 km/h
- Direction of the wind: from the east
To calculate the velocity of the helicopter relative to the ground, we need to consider the vector addition of the helicopter's airspeed and the wind. Since the wind is blowing from the east, we'll subtract its velocity vector from the helicopter's airspeed vector (since the wind is acting in the opposite direction).
To do this, we can break down the airspeed vector into its northward and eastward components.
Since the helicopter is heading south (180 degrees), the northward component will be zero. The eastward component will be the full magnitude of the airspeed vector since the helicopter is heading directly opposite to the east direction.
Breaking down the vectors:
- Airspeed vector: 125 km/h south
- Wind vector: 50 km/h west (since the wind is coming from the east)
Now, let's subtract the wind vector from the airspeed vector:
- North component: 0 km/h
- East component: 125 km/h - 50 km/h = 75 km/h
So, the velocity of the helicopter relative to the ground is 0 km/h north and 75 km/h west.