Answer:
velocity with respect to air as
Vpa = 1.83 m/s
Explanation:
Given data:
Vae = 45.0 m/s
\theta_ae (air with respect to earth) = 23°
\theta_pe (plane with respect to Earth) = 45°
\theta_pa (plane with respect to air) =7°
We have
,
Vpe = Vpa + Vae
substituting each values with corresponding angle we get
Vpe (cos 45i + sin45 j) = Vpa (cos 7i + sin7 j) + 45 (cos 23i + sin23 j)
where,
Vpe - plane velocity with repect to earth
Vpa - planevelocity with respect to air
Vae - air velocity with respect to earth
Solving
Vpe (0.52i + 0.85 j) = Vpa (0.73i + 0.65 j) + 45 (-0.53i - 0.84 j)
considering i terms and j terms separately
Vpe *0.52 = Vpa (0.73 +45 *(-0.53))
Vpe = 1.40 Vpa -45.86
Vpe *0.85 = Vpa (0.65 +45 *(-0.84)
Vpe =0.76Vpa - 44.47
putting one value Vpe in either equation we get :
1.40 Vpa -45.86 = 0.76Vpa - 44.47
velocity with respect to air as
Vpa = 1.83 m/s
