An ant, crazed by the Sun on a hot Texas afternoon, darts overan xy plane scratc
ID: 1737248 • Letter: A
Question
An ant, crazed by the Sun on a hot Texas afternoon, darts overan xy plane scratched in the dirt. The x and y components offour consecutive darts are the following, all in centimeters:(30.0,40.0), (bx,-70.0), (-20.0, cy), (-80.0,-70.0). The overall displacement of the four darts has the xycomponents(-140,-20.0). What are (a) bx and (b) cy?What are the (c) magnitude and (d) angle (relative tothe position direction of the x axis) of the overalldisplacement? An ant, crazed by the Sun on a hot Texas afternoon, darts overan xy plane scratched in the dirt. The x and y components offour consecutive darts are the following, all in centimeters:(30.0,40.0), (bx,-70.0), (-20.0, cy), (-80.0,-70.0). The overall displacement of the four darts has the xycomponents
(-140,-20.0). What are (a) bx and (b) cy?What are the (c) magnitude and (d) angle (relative tothe position direction of the x axis) of the overalldisplacement?
Explanation / Answer
if the overall components are (-140,-20) then you add the x and y components 30+bx+-20+-80=-140 bx=-70 40+-70+cy+-70=-20 cy=80 magnitude is square root of x^2+y^2 sqr rt (-140^2+-20^2)= 141.42 angle theta is tan theta = y/x tan theta = -20/-140 theta= arc tan (-20/-140) = 8.13 degrees