Answer
(a) Answer :
The sum will be smaller than before.
Explanation :
Following example 2.2, figure 1 illustrates the forces angled at $30^{\circ}$ north and south of east. The drawing shows that the arrow representing the vector sum has a length of 13 cm and is directed due east. The magnitude of the sum is, therefore,
$13 cm\times\frac{200 N}{1 cm}=2.6 kN$
Discussion:
Since the angle between the two vectors becomes larger and larger, the magnitude of $F_{S}+F_{B}$ becomes smaller than if they were in the same direction.
Work Step by Step
(b) Answer:
Yes, it is possible for the sum of two forces to be due east, provided the force by Sam is larger than Bob.
Explanation:
Figure 2 illustrates the case where the force by Sam ($F_{S}$) is angled at $10^{\circ}$ north of east and force by Bob ($F_{B}$) is angled at $15^{\circ}$ south of east. Let us assume that both vectors, $F_{S}$ (represented by a grey arrow) and $F_{B}$ (represented by green dashed arrow), have the same magnitude. The arrow representing the vector sum (red dashed arrow) will be directed due southeast. If we reduce the magnitude of $F_{B}$ such that the new vector $F_{B}$ is represented by the black arrow, the arrow representing the vector sum (represented by the blue arrow) will be directed due east.
From the figure, for the vector sum to be directed due east, the vector $ F_{B}$ must have a magnitude of
$5 cm\times\frac{200 N}{1 cm}=1 kN$
