Question

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 34 m/s . The plane is in a 12 m/s wind blowing toward the southwest relative to the earth.

a) Letting x be east and y be north, find the components of v? P/E (the velocity of the plane relative to the earth).

b) Find the magnitude of v? P/E .

c) Find the direction of v? P/E .

Answer 1

Velocity of the plane(V_p) and wind(V_w) are shown in the figure
Now taking the components of the velocity of wind in x and y direction
In x direction
V_wx = -V_wCos 45 = -12Cos45 = -8.485 m/s
V_wy = -V_wSin45 = -12Sin45 = -8.485 m/s
Now, we will take the final velocity in the x and y direction
V_X =-8.485
V_Y = -V_P - 8.485 = -34 -8.485 = -42.485 m/s
hence the magnitude of the velocity will be
V = (V_x² + V_y²)^1/2 = [(-42.485²) + (-8.485²)]^1/2 = 42.324 m/s
Now the direction of the velocity
tan = (V_Y) /V_X
= tan^-1 (-42.485 / -8.485)
= 78.7 from the - Y axis