Question

A force F1 when added to a force F2 =3i-5j gives a resultant force F=-4i .Then F1 is given by

Answer 1

The force $F_{1}$ is given by -7i + 5j.

Given:

Two forces, $F_{1}$ and $F_{2}$

$F_{2}$ = 3i-5j

F = -4i, where $F_{1}$ + $F_{2}$ = F

To Find:

The value of $F_{1}$ .

Solution:

We have been given two forces, $F_{1}$ and $F_{2}$ such that on adding $F_{1}$ to $F_{2}$, we obtain a resultant force F.

i.e. F =  $F_{1}$ + $F_{2}$

Also,

The value of the resultant force F = -4i

The value of the force  $F_{2}$ = 3i - 5j

⇒ -4i =  $F_{1}$ + (3i - 5j)

⇒ $F_{1}$ = -4i - (3i - 5j)

⇒  $F_{1}$ = (-4i - 3i) + 5j

⇒  $F_{1}$ = -7i + 5j.

∴ The force $F_{1}$ is given by -7i + 5j.

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