A particle moves along a straight path through a displacement d = 2.5i + cj while a force F = 8.5i + - 8.5j acts on it. The displacement is measured in meters and the force is measured in Newtons. (Other forces also act on the particle.) What is the value of c if the work done by F on the particle is zero?

Work is defined as the scalar product of force and distance

W=F•d

Given that

F = 8.5i + - 8.5j. + * -=-

F=8.5i-8.5j

d = 2.5i + cj

If the work in the practice is zero, then W=0

therefore,

W=F•ds

0=F•ds

0 = (8.5i - 8.5j) • (2.5i + cj)

Note that

i. i=j. j=k. k=1

i. j=j. i=k. i=i. k=j. k=k. j=0

So applying this

0 = (8.5i - 8.5j) • (2.5i + cj)

0 = (8.5*2.5i. i + 8.5*ci. j - 8.5*2.5j. i-8.5*cj. j)

0=21.25-8.5c

Therefore,

8.5c=21.25

c=21.25/8.5

c=2.5