ivanradoszyce
Member
- Joined
- Oct 18, 2023
- Messages
- 36
- Gender
- Undisclosed
- HSC
- 2018
I came across this problem from the Cambridge Ex 2 book, the Mechanics section.
![Screenshot 2024-08-28 at 4.26.28 PM.png](/data/attachments/44/44003-6c6f8b22a44f23c5c85c4ff2d82a044d.jpg)
Part (d) has me scratching my head. Obviously
cannot be 1. This results in an improper integral.
From part (c)
![](https://latex.codecogs.com/png.latex?\bg_white
\begin{align*}
\dot{y}^2 &= \frac{3g(3 - 2y)}{3 + 2y} \,\,\, \text{which simplifies to } \\
\frac{dt}{dy} &= - \frac{1}{\sqrt{3g}} \sqrt{\frac{1 + \frac{2}{3}y}{1 - \frac{2}{3}y}} \,\,\, \text{where - indicates a decreasing rate }
\end{align*}
)
I can't determine what the
terminal would be if I performed the integration. I thought the upper
terminal could be 3/2 before applying a substitution of
. However that doesn't achieve the desired result. So I'm confused. The answer indicates ![](https://latex.codecogs.com/png.latex?\bg_white \alpha= \frac{1}{4})
Any help appreciated.
![Screenshot 2024-08-28 at 4.26.28 PM.png](/data/attachments/44/44003-6c6f8b22a44f23c5c85c4ff2d82a044d.jpg)
Part (d) has me scratching my head. Obviously
From part (c)
I can't determine what the
terminal could be 3/2 before applying a substitution of
Any help appreciated.