Vector Projection Application - Rolling Cart

Vector Projection Application - Rolling Cart. An application of force vectors in 3D space. Here we look at popular exercise where an object such as a boat, truck, trailer, etc. is sitting on a hill. The question asks how much force is required to hold the object on the hill without rolling backwards.

Help us caption & translate this video!

[johnspence]

For those asking why is x represented by cos18i and y represented by sin18j: If you look at any vector, it can be broken down by its horizontal and its vertical components, forming a right angle triangle, or its x and y, or i, j. When you look at a triangle thats right angled, you use soh cah toa, where cosine of the angle = adj/h. And sin of angle = opp/h. Rewritten, opposite side = sin of angle*h, and adj = cos of angle*h, however we're using a single unit vector where h=1, so the horizontal/x amount can be represented by cos 18i (the angle we're talking about) and the vertical component is sin18j, and those will be your old x, y coordinates. Try it with a hypoteneuse right angle triangle where the h=1, and the corner angle is 18...you will find the horizontal component is 0.951 and the vertical component is 0.309...making the x, y coordinates: 0.951, 0.309 and when we square them both and add them together, we get 1. So you can write ANY single/unit vector as x=cos(angle) i, and y = sin(angle)j

[GooglyCactus]

Thank you so much for the explanation!!! I feel so relieved at having FINALLY understood this type of problem!

[ndngdippchn]

All your lectures are worth it..Thankyou🙏

[cal]

Awesome video. Wish you were my teacher

[lizchatham]

Omg this is exactly the video I've been looking for. <3

[todayiglowup]

why did u treat vector v as a unit vector

[MathCuriousity]

What is a “unit vector” and why and how does he know “V” is a unit vector and how does this help the math?!

[gorgesoros]

Isn't the final answer in vector form?

[MathCuriousity]

He says “v is a “unit vector” and …..it’s on unit circle and has magnitude of one. How do we know v is a unit vector?! And being such, why does that give us 1?!

[herbmiller]

when dealing with a problem like this ex. Why are we looking for the magnitude of the projection?

[lennartweik]

F = mg*sin(teta) = 90*9, 81*sin(18) = 273 N ( SI units ofc ) :)

[gamegamer]

save me twice, once in the midterm and once in the term exam

[lennartweik]

The answer is wrong, the dimension of a force isn't a mass :)