A constant force with vector representation F = i + 2j moves an object along a straight line from the point (2, 4) to the point (5, 7). Find the work done in foot-pounds if force is measured in pounds and distance is measured in feet.
A)6
B)7
C)8
D)9
E)10
F)11
G)12
H)13

Question

Quizplus · Accepted Answer

First, we need to find the displacement vector D, which is the difference between the final and initial positions: D = <5-2, 7-4> = <3, 3> The dot product of the force vector and the displacement vector gives us the work done: W = F · D = (1)(3) + (2)(3) = 9 Therefore, the work done is 9 foot-pounds. The correct answer is D.

A Constant Force with Vector Representation F = I