Answer:
Tarzan will knock her off her limb. (CRASH!)
Explanation:
The difference between a tender embrace or a knock out is derived of a convenient application of the Principle of Energy Conservation, in which a tender embrace mean the absence of kinetic energy and, most specific, speed, when Tarzan arrives to the tree, where Jane is waiting. Tarzan starts at rest. Hence:
[tex]U_{g,A} = U_{g,B} + K_{B}[/tex]
The criteria is depicted as follows:
[tex]K_{B} = U_{g,A} - U_{g,B}[/tex]
[tex]K_{B} = m \cdot g \cdot (h_{A}-h_{B})[/tex]
[tex]\frac{1}{2}\cdot m \cdot v^{2} = m \cdot g \cdot (h_{A}-h_{B})[/tex]
[tex]v = \sqrt{2\cdot g \cdot (h_{A}-h_{B})}[/tex]
Heights are, respectively:
[tex]h_{A} = 20\,m\cdot (1 - \cos 45^{\textdegree})[/tex]
[tex]h_{A}\approx 5.858\,m[/tex]
[tex]h_{B} = 20\,m\cdot (1 - \cos 30^{\textdegree})[/tex]
[tex]h_{B} \approx 2.679\,m[/tex]
The final speed is:
[tex]v = \sqrt{2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (5.858\,m-2.679\,m)}[/tex]
[tex]v\approx 7.896\,\frac{m}{s}[/tex]
Which mean that Tarzan will knock her off her limb. (CRASH!)
