Question

(10%) Problem! 3:1 start walking. The lst leg of my trip I walk dA-145 m at a-12° south of east. The 2nd leg of my trip I walk dB 105 m at θ 29 north of east. On my final leg I walk dc-85 mat θ 63 north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north.

A) Write an expression for the x-component of the final displacement in terms of the given quantities.

B) Write an expression for the y-component of the final displacement in terms of the given quantities.

C) What is the magnitude of my displacement vector (in meters) as measured from the origin?

D) What is the angle of my displacement vector as measured counterclockwise from the +x-axis?

Answer 1

The displacement for the first step can be written as: 145 cos12%-145 sin12*) 141.83-30.15j The displacement for the second step can be written as: 105 cos29 i +105 sin299 j 91.83 i+ 50.9j The third step can be written as: ,--85 cos 63% + 85 sin 63°j -38.6+ 75.7j Adding all three, we get the net displacement. (14 1.83i_ 30.15) + (91.83 і + 50.9) + (-38.6 i + 75.7 j 195.06 i + 96.45 j a) So, the x component of the displacement is 195.06 m b) The y component final displacement is 96.45 m. c) The magnitude of the final displacement is, 阼V (195.06 m) +(96.45 m) = 217.60 m d) The angle made by final displacement is, 195.06 -26.31。