Question #252152

a) An airplane trip involves three legs, with two stopovers. The first leg is due East for 620 km; the second leg is Southeast (45°) for 440 km; and the third leg is at 53° South of West, for 550 km.


i. Draw a figure showing the journey.


ii. What is the plane's total displacement and direction? 


1
Expert's answer
2021-10-18T11:08:55-0400


Along x direction: D1+D2cos45°D3cos53°D_1 + D_2 cos 45° -D_3cos53°

=320+440×cos45°550×cos53°=600.128= 320 + 440 \times cos 45° -550 \times cos53° \\ = 600.128

Along y direction: (D2sin45°+D3sin53°)-(D_2 sin45° +D_3sin53° )

=(440×sin45°+550×sin53°)=750.37DR=(600.128)2+(750.37)2=960.83sinθ=yDR=750.37960.83=0.7809θ=sin1(0.7809)=51.3°= -(440 \times sin45° + 550 \times sin53°) \\ = -750.37 \\ |\vec{D_R}| = \sqrt{(600.128)^2 +(750.37)^2} = 960.83 \\ sin θ = \frac{y}{D_R} = \frac{750.37}{960.83} = 0.7809 \\ θ = sin^{-1}(0.7809) = 51.3°


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