A strong child pulls a sled with a force of 108 N at an angle of 33.6° above the horizontal. Find the vertical and horizontal components of this pull.
F = 108N @ 33.6 DEG.
Fh = 108*cos33.6 = 90N.
Fv = 108*sin33.6 = 59.8N.
To find the vertical and horizontal components of the force, we can use trigonometry.
The vertical component can be found using the sine function, and the horizontal component can be found using the cosine function.
Step 1: Identify the given information.
- Magnitude of the force: 108 N
- Angle above the horizontal: 33.6°
Step 2: Calculate the vertical component.
To find the vertical component, we use the sine function. The sine of an angle is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the vertical component, and the hypotenuse is the magnitude of the force.
Vertical component = Magnitude of the force * sin(angle)
Vertical component = 108 N * sin(33.6°)
Now we need to find the value of sin(33.6°). You can use a scientific calculator or an online calculator to find the sine of the given angle.
sin(33.6°) ≈ 0.556
Therefore, the vertical component is:
Vertical component = 108 N * 0.556
Vertical component ≈ 59.97 N (rounded to two decimal places)
Step 3: Calculate the horizontal component.
To find the horizontal component, we use the cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side is the horizontal component, and the hypotenuse is the magnitude of the force.
Horizontal component = Magnitude of the force * cos(angle)
Horizontal component = 108 N * cos(33.6°)
Using a calculator, find the value of cos(33.6°).
cos(33.6°) ≈ 0.831
Therefore, the horizontal component is:
Horizontal component = 108 N * 0.831
Horizontal component ≈ 89.65 N (rounded to two decimal places)
So, the vertical component of the pull is approximately 59.97 N, and the horizontal component is approximately 89.65 N.