Answer to Question #279348 in Mechanics | Relativity for btch

Question

The nose of an ultralight plane is pointed south, and its airspeed indicator shows 35 m/s. The plane is in a 10-m/s wind blowing toward the southwest relative to the earth. (a) In a vector addition diagram, show the relationship of →vP/E (the velocity of the plane relative to the earth) to the two given vectors. (b) Letting x be east and y be north, find the components of →vP/E. (c) Find the magnitude and direction of →vP/E.

Answer 1

a)

b)

$v_{P/Ex}=v_wcos45\degree=-10/\sqrt 2=-7.07$ m/s

$v_{P/Ey}=v_wcos45\degree+v_P=-7.07-35=-42.07$ m/s

v_P is speed on airspeed indicator,

v_w is wind speed

c)

$v_{P/E}=\sqrt{v_{P/Ex}^2+v_{P/Ey}^2}=\sqrt{(10/\sqrt 2)^2+(10/\sqrt 2+35)^2}=42.66$ m/s

angle to x-axis:

$cos\alpha=v_{P/Ex}/v_{P/E}=-7.07/42.66=-0.1657$

$\alpha=260\degree$

direction is $10\degree$ west to south