Tarzan

Tarzan, weighing m = 90 kg, tries to cross the river by swinging with a vine hanging from a tree leaning over the river. Liana has a length l = 12 m. The speed of the Tarzan in the lowest swing position is v = 8 m/s. Tarzan doesn't know that the liana will break when stretched with a force of F = 1000 N. Will Tarzan reach the other side of the river safely?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} m=90\text{kg} \\ l=12\text{m} \\ v=8\text{m/s} \\ F=1000\text{N} \\ g=9.81{\text{m/s}}^2 \\ G=m\cdot g=90\cdot 9.81=\frac{8829}{10}=882\frac{9}{10}=882.9\text{N} \\ {F}_1=\frac{m\cdot v^2}{l}=\frac{90\cdot 8^2}{12}=480\text{N} \\ {F}_2=F_1+G=480+\frac{8829}{10}=\frac{480\cdot 10}{10}+\frac{8829}{10}=\frac{4800}{10}+\frac{8829}{10}=\frac{4800+8829}{10}=\frac{13629}{10}=1362.9\text{N} \\ {F}_2>F \\ x=0 \end{gathered}$$

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