5N 30degrees and 10N 45 degrees 10N at 3rd quadrant.
find the direction of resultant force.(in degrees)
a.)2.74
b.)-4.57
c.)-2.74
d.)5.33
e.)4.57
To find the direction of the resultant force, we can use the concept of vector addition.
First, let's convert the given forces into vector form using their magnitudes and angles.
The force 5N at 30 degrees can be expressed as \(5N \angle 30^\circ\).
The force 10N at 45 degrees can be expressed as \(10N \angle 45^\circ\).
Now, let's represent these vectors in the Cartesian coordinate system.
The vector \(5N \angle 30^\circ\) can be split into its x and y components:
x = 5N * cos(30°)
= 5N * 0.866
= 4.33N
y = 5N * sin(30°)
= 5N * 0.5
= 2.5N
So, the vector \(5N \angle 30^\circ\) can be represented as (4.33N, 2.5N) in the Cartesian coordinate system.
Similarly, the vector \(10N \angle 45^\circ\) can be split into its x and y components:
x = 10N * cos(45°)
= 10N * 0.707
= 7.07N
y = 10N * sin(45°)
= 10N * 0.707
= 7.07N
So, the vector \(10N \angle 45^\circ\) can be represented as (7.07N, 7.07N) in the Cartesian coordinate system.
To find the resultant force, we can add the x and y components of both vectors:
x-component: 4.33N + 7.07N = 11.4N
y-component: 2.5N + 7.07N = 9.57N
Now, using the x and y components, we can find the magnitude and the angle of the resultant force.
The magnitude of the resultant force is given by the Pythagorean theorem:
magnitude = sqrt((11.4N)^2 + (9.57N)^2)
= sqrt(130.68N^2 + 91.4649N^2)
= sqrt(222.1449N^2)
= 14.9N (approximately)
The angle of the resultant force can be found using the inverse tangent function:
angle = atan(9.57N / 11.4N)
= atan(0.83728)
= 40.39 degrees (approximately)
Therefore, the direction of the resultant force is approximately 40.39 degrees.
However, in the given answer choices, there isn't an exact match for the calculated angle. The closest option is "c.)-2.74."