Cambridge 3unit year 12 textbook Chapter 7F Question 7c (1 Viewer)

michaeljennings · Apr 26, 2015

Would someone be able to show worked solutions for Chapter 7F, question 7c (page 269) cheers

InteGrand · Apr 26, 2015

michaeljennings said:
Would someone be able to show worked solutions for Chapter 7F, question 7c (page 269) cheers

$This is the one about a particle moving around a circle, right?$

$From part (a), we know that $\theta = \tan ^{-1}t + \frac{\pi}{4}$, for $t\geq 0$.$

$Then since the inverse tan function has range $0\leq \tan ^{-1} t< \frac{\pi}{2}$ for all $t\geq 0$, clearly $0+\frac{\pi}{4} \leq \theta < \frac{\pi}{2}+ \frac{\pi}{4}\Rightarrow \frac{\pi}{4}\leq \theta < \frac{3\pi}{4}$. Since the particle starts at $\theta = \frac{\pi}{4}$, and asymptotically approaches $ \theta = \frac{3\pi}{4}$ as $t\to \infty$, the particle never rotates through an angle more than: $\text{limiting angle}- \text{initial angle}=\frac{3\pi}{4} - \frac{\pi}{4}=\frac{\pi}{2}$.$

michaeljennings · May 3, 2015

cheers

Cambridge 3unit year 12 textbook Chapter 7F Question 7c (1 Viewer)

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