Question

There are two forces each of magnitude 10 units. One inclined at an anlge of 30° and the other at an angle of 135° to the positive direction of x-axis. The x and y components of the resultant are respectively.

Answer 1

Final Answer :
F(x) resultant = 5(√3-√2)
F(y) resultant = 5(√2+1)

Steps :
1) We will take components of both these forces individually.
2) Then, add these components vectorially with direction in particular x and y.

For calculation see pic.

Answer 2

Let first force be F

1

and its magnitude =10

Let first force be F

2

and its magnitude =10

Now,

Angle F

1

is making with positive x-axis =30

o

Angle F

2

is making with positive x-axis =135

o

Angle between F

1

and F

2

=135−30

=105

o

Since both the vectors have equal magnitude the resultant will make

2

105

o

.

Angle with both the vector =52.5+30=82.5

o

Now, magnitude of resultant =

100+100+200cos105

=12.175 unit

Now,

X component =∣R∣cosθ

=12.175×cos82.5

=12.175×0.13

=1.583

Y component =∣R∣sinθ

=12.175×sin82.5

=12.175×0.99

=12.05