p07_054.pdf

54. (a) With SI units (and three signiﬁcant ﬁgures) understood, the object’s displacement is

d = d f −

d i =

−

8i+6j+2k .

Thus, Eq. 7-8 gives

W = F

d =(3)(

−

8) + (7)(6) + (7)(2) = 32 . 0J .

(b) The average power is given by Eq. 7-42:

P avg = W

= 32

=8 . 00 W .

2) 2 +5 2 =6 . 16 m,

and the magnitude of the distance from the coordinate origin to the ﬁnal position is d f = (

−

5) 2 +4 2 +7 2 =

9 . 49 m. Their scalar (dot) product is

d i

d f =(3)( − 5) + ( − 2)(4) + (5)(7) = 12 . 0m 2

Thus, the angle between the two vectors is

φ =cos − 1 d i

d f

d i d f

=cos − 1 12 . 0

(6 . 16)(9 . 49)

which yields φ =78 ◦ .

−