Step-by-step explanation:
Below is an attachment containing the solution.
[tex]\to \Sigma fx=0 \\\\\to \frac{mv^2}{r}= N \sin \theta + V | S N \cos \theta..............(1) \\\\\to \Sigma fy =0 N \cos \theta - V| s N \sin \theta mg ......................(2)\\\\[/tex]
solving an equation 1 and 2 for maximum speed:
[tex]\to V_{max} = \sqrt{ \frac{r g (\sin \theta + v | s \cos \theta)}{\cos \theta - v|s \sin \theta}} \\\\[/tex]
[tex]= \sqrt{ \frac{500 \times 32 (\sin 30 + .2 \times \cos 30)}{\cos 30 - .2 \times \times \sin 30}} \\\\= \sqrt{ \frac{500 \times 32 (\frac{1}{2} + .2 \times \frac{\sqrt{3}}{2})}{ \frac{\sqrt{3}}{2} - .2 \times \frac{1}{2}}} \\\\= \sqrt{ \frac{16000 (\frac{1}{2} + \frac{1.73}{10})}{ \frac{1.73}{2} - \frac{1}{10}}} \\\\= \sqrt{ \frac{16000 (0.5 + 0.173)}{ 0.865 -0.1}} \\\\= \sqrt{ \frac{10768}{ 0.765 }} \\\\= \sqrt{ 14075.8165} \\\\=118.64 \ \frac{ft}{see}\\\\[/tex]
Therefore, the maximum speed "118.64".
Learn more about the maximum speed:
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