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Problem 30 Medium Difficulty

If a child pulls a sled through the snow on a level path with a force of 50 N exerted at an angle of $ 38^\circ $ above the horizontal, find the horizontal and vertical components of the force.

Answer

horizontal $\approx 39.4 \mathrm{N} \quad$ vertical $\approx 30.8 \mathrm{N}$

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Video Transcript

so in this problem, or you'll be looking at vectors. And what we see is that, um the sled is pulled through the snow with a force of 50 Newtons exert an angle of 38 degrees s. So what we have is sort of like a right triangle in which we have a high pop news. Say it looks something like this and then cut off a tsum point. This is 50 Newtons, some vector on that's going to be I'm essentially equivalent two this vector and this vector two vectors, one going right and one going up. So we see that the magnitude of the vector, which is the force, is 50 Newtons. So that means that we'll have a equal to our coast science data and be equal to our find data. We know that our is the magnitudes. That'll be 50. I'm the co sign of 38 and this is in degrees, so we'll get 39.4 degrees, and then this is going to be 50 again because that's the magnitude and 38 degrees. So we'll get 30.8, you know, approximately s O. That means that horizontally, um, it would be 39.4 Newtons at vertically would be 30.8 minutes