Nathaniel pulls a sled along level ground with a force of 30 newtons on the rope attached to the sled. If the rope makes an angle of 20 degrees with the ground when it is pulled taught, find the horizontal and vertical components of the force. Round to the nearest tenth.
Another one of those word problems. Thanks for all of your help!
Even easier.
Did you make a diagram?
the 30 N would be the hypotenuse, and you are finding the opposite side (vertical) and the adjacent side (horizontal)
I didn't make any diagram
To find the horizontal and vertical components of the force, we can use trigonometry.
The horizontal component of the force, denoted as Fx, can be found by multiplying the force by the cosine of the angle.
Fx = Force * cos(angle)
Substituting the values given:
Fx = 30 N * cos(20°)
Calculating Fx:
Fx ≈ 30 N * cos(20°) ≈ 30 N * 0.9397 ≈ 28.2 N (rounded to the nearest tenth)
The vertical component of the force, denoted as Fy, can be found by multiplying the force by the sine of the angle.
Fy = Force * sin(angle)
Substituting the values given:
Fy = 30 N * sin(20°)
Calculating Fy:
Fy ≈ 30 N * sin(20°) ≈ 30 N * 0.3420 ≈ 10.3 N (rounded to the nearest tenth)
Therefore, the horizontal component of the force is approximately 28.2 N, and the vertical component of the force is approximately 10.3 N.
To find the horizontal and vertical components of the force, we will use some trigonometry.
The horizontal component of the force is given by the formula F * cos(theta), where F is the magnitude of the force and theta is the angle between the force and the horizontal direction.
In this case, the magnitude of the force is 30 N and the angle theta is 20 degrees.
So, the horizontal component of the force is:
horizontal component = 30 N * cos(20 degrees)
Using a scientific calculator, we can find that the cosine of 20 degrees is approximately 0.9397.
Therefore, the horizontal component of the force is:
horizontal component = 30 N * 0.9397 = 28.19 N (rounded to the nearest tenth)
The vertical component of the force is given by the formula F * sin(theta), where F is the magnitude of the force and theta is the angle between the force and the horizontal direction.
In this case, the magnitude of the force is 30 N and the angle theta is 20 degrees.
So, the vertical component of the force is:
vertical component = 30 N * sin(20 degrees)
Using a scientific calculator, we can find that the sine of 20 degrees is approximately 0.3420.
Therefore, the vertical component of the force is:
vertical component = 30 N * 0.3420 = 10.26 N (rounded to the nearest tenth)
To summarize:
The horizontal component of the force is approximately 28.2 N.
The vertical component of the force is approximately 10.3 N.