How long is the incline in the following case: A rope is attached to a 50.0-kg crate to pull it up a frictionless incline with a 30 degree angle at a constant speed to a height of 3 meters.

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The problem states that the incline forms an angle of 30 degree and rises to a height of 3m. We need to find the height of the incline. I do not know what you mean by w parallel and w perpendicular. Actually we do not need of that information.

The length of the incline can be determined just from the information that the incline forms an angle of 30 degrees and the height reached at its end is 3m.

We have a perpendicular triangle here, with the length of the hypotenuse = length of the incline = L and the length of the side opposite the 30 degree angle as 3 m

sin 30 = 0.5 = 3/L

=> L = 3 / 0.5

=> L = 6m

Therefore the incline has a length of 6 m.

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