Recent content by ItsukaKitto

Taking modulo 8 shortens the proof a lot! Somehow it wasn't immediately obvious to me 😅. Thanks for letting me know there exists a much simpler and general way to go about such problems.

My take on problem 15: In all seriousness, if this proof works, it is the strangest, most hand wavy proof I've ever done. I am not aware whether arguments involving infinity are commonly used in such problems, let alone whether they are rigorous enough.

Ah yes, they're only a list of permissible values, the actual solutions I think must be a subset of these... ##(0,\sqrt{2}) , (0, -\sqrt{2})## work but the other values don't seem to work.

I know one way to solve the trigonometric problem, only that it happens to be just etotheipi 's approach, but done...(I hope) correctly: Adding the equations we see that we get an inequality in ## A = x^2 + y^2 ## , namely ##cos^4 (x) + sin^4(x) = A(A-4) + 5 <= 1 ## But we see the greatest value...

For the first problem in the high school section, I think one can use induction (Don't know if this has been done already)...noting that for n=1 the solution is trivial i.e. a1 + b1 = a + b, and assuming the statement is true for n = m, ##(a_1^2 + b_1^2)...(a_m^2 + b_m^2) = (a^2 + b^2) ## , we...

For the sake of conserving momentum here, I think that's a reasonable assumption. Thank you for your help.

I see, so would I have to assume the blocks stick together through the entire time the smaller one is on the curved part? Most likely they would have different velocities in that part, and I think whether they will stick together here, depends on the geometry of the big block too. Is this true?

In the curved part, the normal force would have a horizontal component, and the lower block will have a constant velocity in the horizontal direction...then I suppose I can use momentum conservation to find it. I'm not sure however, will the horizontal velocity of both the blocks be the same...

Thanks for replying, I've a few questions... It's not possible for the normal force to cause the lower block to have a horizontal velocity, right? Do you think the "most accurate" answer should actually be v^2/2g then, assuming no friction? In saying that the block should have enough initial...

Diagram attached at the endI personally think there's something wrong with this question, and I'd like if someone can tell me whether it's the question that is wrong or my approach. If I attempt the solution thinking that M should be stationary, the solution is simple. 0 - 1/2 mv^2 = -mgh...