Question

the greater and least resultant of two forces are 9 newtons and 5 newtons if they are applied at 60 degrees the magniyude of the resultant

Answer 1

$F_1 = 9$ Newtons

$F_2 = 5$ Newtons

For greatest magnitude, both the forces should act in the same direction and will add up.

$F (Greatest) = F_1 + F_2$

F (Greatest) = 9 + 5 = 14 Newtons

For smallest magnitude, both the forces should act in the opposite direction and will be subtracted from each other.

F (Smallest) = 9 - 5 = 4 Newtons

Now, when the angle between them is 60°

F (60°) $=\sqrt{5^2 + 9^2 + 2 \times 5 \times 9 \times Cos 60}$

F (60°) $=\sqrt{81 +25 + 45}$

F (60°) = 12.28 Newtons.