An airplane is heading 20degree north flying at 200km/hr relative to the air. Simultaneously the wind carries the plane 10degree, east of south at the speed of 60km/hr. (a) find the velocity of the plane relative to the ground. (b) find the component (east and south) of the velocity of the plane relative to air and of the air relative to the ground
Do you mean 20o N. of E. or N. of
w. or what do you mean?
just 20oN
To find the velocity of the plane relative to the ground, we can break down the velocities into their north-south and east-west components.
(a) Velocity of the plane relative to the ground:
Let's denote the north direction as positive and the east direction as positive.
The velocity of the plane relative to the air can be broken down into its north-south (v_air_NS) and east-west (v_air_EW) components:
v_air_NS = 200 km/hr * cos(20°)
v_air_EW = 200 km/hr * sin(20°)
The velocity of the wind can also be broken down into its north-south (v_wind_NS) and east-west (v_wind_EW) components:
v_wind_NS = 60 km/hr * sin(10°)
v_wind_EW = 60 km/hr * cos(10°)
To find the velocity of the plane relative to the ground, we add the velocities of the plane relative to the air and the wind:
v_plane_NS = v_air_NS + v_wind_NS
v_plane_EW = v_air_EW + v_wind_EW
The velocity of the plane relative to the ground can be found using Pythagoras' theorem:
v_plane_ground = √(v_plane_NS^2 + v_plane_EW^2)
(b) Components of the velocity of the plane relative to air and the air relative to the ground:
From the calculations above, we have already found the components of the plane's velocity relative to the air (v_air_NS and v_air_EW).
To find the components of the air's velocity relative to the ground (v_air_ground_NS and v_air_ground_EW), we subtract the wind's velocity components from the plane's velocity components:
v_plane_ground_NS - v_wind_NS = v_air_ground_NS
v_plane_ground_EW - v_wind_EW = v_air_ground_EW
Thus, the components of the velocity of the plane relative to the ground are:
(a) v_plane_ground = √(v_plane_NS^2 + v_plane_EW^2)
(b) v_air_ground_NS = v_plane_ground_NS - v_wind_NS
v_air_ground_EW = v_plane_ground_EW - v_wind_EW
Now you can substitute the given values and solve the equations to find the specific numerical values.