A pilot wants to fly a plane east at a velocity of 400.0 km/hr with respect to the ground. A 50.0 km/hr wind is blowing southward. With respect to the air, what velocity must the pilot maintain?
X = 400 km/h.
Y = 50 km/h.
V = sqrt(X^2+Y^2).
Tan A = Y/X = (-50)/400 = -0.125, A = -7.125o = 7.125o S. of E.
To determine the velocity the pilot must maintain with respect to the air, we need to consider the wind speed and direction.
Given:
- The velocity of the plane with respect to the ground is 400.0 km/hr eastward.
- The wind velocity is 50.0 km/hr southward.
We can break down the velocity of the plane with respect to the air into two components: horizontal (east-west) and vertical (north-south) components.
The horizontal component of the plane's velocity with respect to the air is unaffected by the wind, as the pilots want to maintain an eastward direction. Therefore, the horizontal component remains 400.0 km/hr.
The vertical component of the plane's velocity with respect to the air is affected by the wind blowing southward. We need to subtract the wind velocity component to ensure the plane maintains its altitude.
Let's calculate the vertical component of the plane's velocity with respect to the air:
Vertical component = Plane's velocity - Wind velocity
Vertical component = 0 km/hr (altitude is maintained)
Therefore, the pilot must maintain a velocity of 400.0 km/hr eastward with respect to the air to compensate for the 50.0 km/hr southward wind velocity.
To determine the velocity the pilot must maintain with respect to the air, we need to consider the vector addition of the velocity of the plane (with respect to the ground) and the velocity of the wind.
Given:
Velocity of the plane with respect to the ground = 400.0 km/hr (eastward)
Velocity of the wind = 50.0 km/hr (southward)
To find the velocity of the plane with respect to the air, we can use vector addition. Let's break down the velocity vectors into their eastward and northward components:
Velocity of the plane with respect to the ground:
- Eastward component = 400.0 km/hr (since the plane is flying eastward)
- Northward component = 0 km/hr (since the plane is not flying northward)
Velocity of the wind:
- Eastward component = 0 km/hr (since the wind is not blowing eastward)
- Northward component = -50.0 km/hr (since the wind is blowing southward)
Now, add the respective components of the two vectors to get the velocity of the plane with respect to the air:
Eastward component (plane) + Eastward component (wind) = 400.0 km/hr + 0 km/hr = 400.0 km/hr
Northward component (plane) + Northward component (wind) = 0 km/hr + (-50.0 km/hr) = -50.0 km/hr
So, the velocity of the plane with respect to the air must be 400.0 km/hr eastward and 50.0 km/hr northward.