a wagon is being pulled by a rope that makes at 25o angel with the ground . thee person is pulling with a force of 103N along the rope . determine the horizontal and vertical components of the vector
Fap = 103N @ 25Deg.
X = 103*cos25.
Y = 103*sin25.
To determine the horizontal and vertical components of the vector, we first need to understand the concept of trigonometry. Trigonometry deals with the relationships between the angles and sides of triangles.
In this case, we can use trigonometry to break down the force pulling the wagon into its horizontal and vertical components.
Let's denote the angle between the rope and the ground as θ, which is given as 25o.
The horizontal component represents the force acting parallel to the ground, while the vertical component represents the force acting perpendicular to the ground.
To determine the horizontal component (F_h), we use the formula:
F_h = F * cos(θ)
where F is the given force of 103N, and cos(θ) represents the cosine of the angle θ.
Let's substitute the values:
F_h = 103N * cos(25o)
Now, using a calculator or trigonometry table, we find that cos(25o) is approximately 0.9063.
F_h = 103N * 0.9063
≈ 93.52N (rounded to two decimal places)
So, the horizontal component of the vector is approximately 93.52N.
Now, to determine the vertical component (F_v), we use the formula:
F_v = F * sin(θ)
where F is the given force of 103N, and sin(θ) represents the sine of the angle θ.
Let's substitute the values:
F_v = 103N * sin(25o)
Using a calculator or trigonometry table, we find that sin(25o) is approximately 0.423.
F_v = 103N * 0.423
≈ 43.53N (rounded to two decimal places)
So, the vertical component of the vector is approximately 43.53N.
Therefore, the horizontal component is approximately 93.52N, and the vertical component is approximately 43.53N.