Answer to Question #246789 in Physics for Bellinson

Question #246789

an airplane is flying in calm air 80 m/s bearing 40 degrees when it suddenly encounters a 20 m/s wind bearing 140. Determine the resultant velocity of the airplane.


1
Expert's answer
2021-10-05T10:05:54-0400

v1x=80cos40°=61.28 (m/s)v_{1x}=80\cdot \cos40°=61.28\ (m/s)

v1y=80sin40°=51.42 (m/s)v_{1y}=80\cdot \sin40°=51.42\ (m/s)


v2x=20cos140°=15.32 (m/s)v_{2x}=20\cdot \cos140°=-15.32\ (m/s)

v2y=20sin140°=12.86 (m/s)v_{2y}=20\cdot \sin140°=12.86\ (m/s)


vx=61.2815.32=45.96 (m/s)v_x=61.28-15.32=45.96 \ (m/s)

vy=51.42+12.86=64.28 (m/s)v_y=51.42+12.86=64.28 \ (m/s)


v=45.962+64.282=79 (m/s)v=\sqrt{45.96^2+64.28^2}=79\ (m/s)

α=tan164.2845.96=54.43°\alpha=\tan^{-1}\frac{64.28}{45.96}=54.43°




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