High School

The magnitudes of the vectors are [tex]F = 75 \, \text{N}[/tex] and [tex]P = 66 \, \text{N}[/tex]. They act at angles [tex]\theta = 45^\circ[/tex] and [tex]\phi = 54^\circ[/tex]. Find the angle between the resultant of the two forces and the x-axis in degrees.

Answer :

The angle between the resultant vector and the x-axis is approximately 43.5 degrees.

The x-component of the resultant vector R can be found by adding the x-components of the two vectors:

Rx = F cos(theta) + P cos(phi)

Substituting the values, we get:

Rx = 75 N cos(45 deg) + 66 N cos(54 deg)

Rx ≈ 114.8 N

The y-component of the resultant vector R can be found by adding the y-components of the two vectors:

Ry = F sin(theta) + P sin(phi)

Substituting the values, we get:

Ry = 75 N sin(45 deg) + 66 N sin(54 deg)

Ry ≈ 103.7 N

The magnitude of the resultant vector R can be found using the Pythagorean theorem:

|R| = √(Rx² + Ry²)

Substituting the values we calculated, we get:

|R| = √(114.8 N)² + (103.7 N)²

|R| ≈ 152.8 N

The angle between the resultant vector R and the x-axis can be found using the inverse tangent function:

θ = tan⁻¹(Ry / Rx)

Substituting the values we calculated, we get:

θ ≈ 43.5 deg

Learn more about vector here:

https://brainly.com/question/19802988

#SPJ11