Answer to Question #252152 in Optics for Josh

Question

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? 

Answer 1

Along x direction: $D_1 + D_2 cos 45° -D_3cos53°$

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

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

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