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**superdude** Tarzan is in the path of a pack of stampeding elephants when Jane swings in on a rope vince, careing Tarzan to safety. The length of the vince is 25m and Jane starts her swing with the rope horizontal. If Jane’s mass is 54kg and Tarzan’s is 82 kg, to hwat hieght above the ground will the pair swing after she rescues him? Assume rope is vertical when she grabs him.

Initially $\displaystyle U_1=mgh=54kg(9.81m/s^2)25m=13243.5 J$

All this potential energy is converted to kinetic energy when Jane grabs Tarzan. So $\displaystyle K_2=U_1=13243.5J=\frac{1}{2}m_Jv^2 \Longleftrightarrow v=\sqrt{\frac{2U_1}{m_J}}=\sqrt{\frac{2(13243.5J)} {54kg}}=22.147m/s$

When Jane and Tarzan come to rest $\displaystyle U_3=\frac{1}{2}(m_J+m_T)v_2^2=(m_T+m_J)gh_3 \Longleftrightarrow h_3 = \frac{\frac{1}{2}(m_J+m_t)^2v_2^2}{(m_J+m_T)g}=347 5m$

**And that’s the wrong answer.**