Question

An ant, crazed by the Sun on a hot Texas afternoon, darts over an xy plane scratched in the dirt. The x and y components of four consecutive darts are the following, all in centimeters: (30.0, 38.0), (bx, -68.0), (-23.0, cy), (-83.0, -68.0).The overall displacement of the four darts has the xy components (-140, -19.0).What are (a) bx and (b) cy? What are the (c) magnitude and (d) angle (counterclockwise from the positive direction of the x axis) of the overall displacement?

Answer 1

Dx = Component of the displacement in the x direction = 30 + bx - 23 - 83 = -140. Now from this simple equation we can solve for bx and get: bx = -140 + 83 + 23 -30 = -64. Similarly we can solve for cy from the Dy-component balance, as follows:

Dy =Component of the displacement in the y-direction= 38 - 68 +cy - 68 = -19,

from where cy= -19 +68 +68 -38 = 79.

Now The magnitud of the displacement is given by the expression: D (magnitud) = Which is equal to 141.28 cm.

Finally the direction of the Displacement will be determined by the following expression:

so 187.72 degrees is the counter clockwise direction of the displacement with respect to te plus x axis.

Notice that we need to add up 180 degrees to our small angle 7.72 degrees because the displacement vector is right on the third quadrant as you can see from its x-y components being both negative, and because they asked us for a counterclock direction, also.