Question

darts over an xy plane scratched in the dirt. The x and y components of four consecutive darts are the following, all in centimeters: (25.0, 47.0), (b -64.0), (-19.0, cy) -32.0).What are (a) b, and (b) Gy? What are the (c) magnitude an displacement? 53.0).The overall displacement of the four darts has the xy components (-140, d (d) angle (counterclockwise from the positive direction of the x axis) of the overall (a) Number m75 (b) Numberr 20 (c) Number 102.59 (d) Number 1143.02

Answer 1

We are given the four displacements (x₁,y₁)=(25.0,47.0) cm;(x₂,y₂)=(b_x,-64.0) cm;(x₃,y₃)=(-19.0,c_y) cm;(x₄,y₄)=(-81.0,-53.0) cm.

The sum of the 4 displacements gives the resultant displacement i.e.(x,y)=(25+b_x-19-81,47-64+c_y)=(-140,-32) cm.

Therefore 25+b_x-19-81=-140 cm i.e b_x=-65 cm. Also 47-64+c_y-53=-32 cm. i.e. c_y=38 cm.

The ant is initially at the position (25.0,47.0) cm and finally at (-140,-32 ) cm.Thus the net displacement is (-140-25,-32-47) cm=

(-165,-79) cm.

The magnitude of the overall displacement =$\sqrt{(-165)^{2}+(-79)^{2}}=183 cm$ and the angle $\theta =tan^{-1}(y/x)=tan^{-1}(-79/-165)=tan^{-1}0.48=25.6^{0}$ with the negative x-axis or 180⁰+25.6⁰=205.6⁰ counterclockwise from the positive x-axis.