Question

The resultant of two forces 10N and 15N acting along +x and -x axes respectively is...?

Answer 1

Since, the vectors are in opposite direction;

R =

\sqrt{ {x}^{2} + {y}^{2} + 2xy \cos( 180) } = \sqrt{x {}^{2} + {y}^{2} - 2xy}

x

2

+y

2

+2xycos(180)

=

x

2

+y

2

−2xy

\sqrt{100 + 225 - 300} = 5

100+225−300

=5

The resultant will be closer to the vector of larger magnitude.

Thus, 5N along -ve X-axis.

Answer 2

Explanation:

It is given that,

Force 1, $F_1=10\ N$ (along +x axis)

Force 2, $F_2=15\ N$ (along -x axis)

We need to find the resultant of two forces. Let the resultant is F. The angle between the both forces are 180 degrees. There resultant is given by :

$F=F_1-F_2$

F = 10 N - 15 N

F = -5 N

So, the resultant force is 5 N in -x axis. Hence, this is the required solution.