Chapter 5, Problem 92GP

To determine

To find: The angle made by fishing line with vertical.

Answer to Problem 92GP

  $76°$

Explanation of Solution

Given Data:

  $\mathcal{l}=0.25$ m

  $T=0.50$ sec

Formula Used:

  $\begin{array}{c}{F}_{\text{T}}\sin \theta =\frac{m{v}^2}{r}\\ \left(\frac{mg}{\cos \theta }\right)\sin \theta =\frac{m{v}^2}{r}\\ g\left(\frac{\sin \theta }{\cos \theta }\right)=\frac{{\left(\frac{2\pi L\sin \theta }{T}\right)}^2}{L\sin \theta }\\ g\left(\frac{\sin \theta }{\cos \theta }\right)=\frac{4{\pi }^{2}L\sin \theta }{T^2}\\ \cos \theta =\frac{g{T}^2}{4{\pi }^{2}L}\\ \theta ={\cos }^{-1}\left(\frac{g{T}^2}{4{\pi }^{2}L}\right)\end{array}$

Calculation:

Substituting the values

  $\sec \theta =\frac{4{\pi }^2\left(0.25\right)}{{\left(0.5\right)}^2\times 10}$

  $\Rightarrow \theta =76°$

Conclusion:

Therefore the angle with vertical is $76°$ .