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Find a link to an explanation using Manim. Projectile Motion with Quadratic Drag.

Thanks tywebb, that's exactly what I got. I appears the answer at the end of the text is incorrect. Frustrating to say the least.

I came across this problem from the Cambridge Ex 2 book, the Mechanics section. Part (d) has me scratching my head. Obviously \alpha cannot be 1. This results in an improper integral. From part (c) \begin{align*} \dot{y}^2 &= \frac{3g(3 - 2y)}{3 + 2y} \,\,\, \text{which simplifies to }...

Any change of putting a link so I can see the paper?

Thanks.... I like the question!

Hi, As a matter of curiosity, where did this question come from?

Substitute x = 1 into the binomial equation call call it 1. Substitute x = - 1 into another binomial equation call call it 2. Add the 2 equations. Noting when you add an even number + odd number = odd number. The 'odd' binomial terms cancel and the 'even' terms are doubled. Hope that is a...

Hi, Are you after a solution to this problem as well?

This may help. Divide each term by z^2, then collect 'like' terms i.e 5(z^2 + z^{-2}) - 11(z + z^{-1} ) + 16 = 0. Then use part (a).

Are they pds of hard copies. Yes, I'm interested.

Thank-you so much. Where can I obtain the ebooks?

Hi all, I really 'enjoy' (if that's the right word) analyzing the Mathematics syllabi of Unit 3/4 mathematics of the 1970s/1980s. I was wondering what text books were using for unit 3/4 during this period. I know in Victoria, at year 12 level, Fitzpatrick & Gailbraith used Purer and Applied...

Hi all, I believe Conics was a topic in Extension 2 a while ago. I was just wondering if anyone had any old PDFs of Extension 2 text books that covered this topic. It more just form my personal interest that anything else. I wold really like to know how it was covered. Thanks

As a matter of interest, where does this question come from?

Here is the solution written in Latex.

Yes, that's the way I did it.

This looks very similar to the following problem: \begin{align*} \text{Given} \\ I_n &= \int \frac{x^n}{1 + x^2} dx \\ \text{show} \\ I_n &= \dfrac{x^{n - 1}}{n - 1} - I_{n - 2} \\ \text{From this expression $I_{n-2} = \int \frac{x^{n-2}}{1 + x^2} dx$ is required. }\\\\ \text{We can get...

Here is part a) and b) written in Latex. I'll post part c) soon. For c) use Vieta's formula. Attached are full solutions + a file about Vieta's formula for cubics.

This may help. The PDF was written using Latex.

The solution in Latex: \begin{align*} \text{Consider $I_n = \int_0^{\sqrt{3}}(3 - x^2)^n dx$} \\[5mm] \text{Using integration by parts } \\[5mm] u &= (3 - x^2)^n \hspace{60pt} v' = 1 \\[5mm] u' &= n(3 - x^2)^{n-1} \cdot -2x \hspace{20pt} v = x \\[5mm] I_n &= uv' - \int...