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# A wagon with two boxes of Gold, having total mass 300 kg, is cutloose from the hoses by an outlaw when the wagon is at rest 50m upa 6.0 degree slope.

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A wagon with two boxes of Gold, having total mass 300 kg, is cutloose from the hoses by an outlaw when the wagon is at rest 50m upa 6.0 degree slope. The outlaw plans to have the wagon roll downthe slope and across the level ground, and then fall into thecanyon where his confederates wait. But in a tree 40m from thecanyon edge wait the Lone Ranger (mass 75.0kg) and Tonto (mass60.0kg). They drop vertically into the wagon as it passes beneaththem. a) if they require 5.0 s to grab the gold and jump out, willthey make it before the wagon goes over the edge? b) When the twoheroes drop into the wagon, is the kinetic energy of the system ofthe heroes plus the wagon conserved? If not, does it increase ordecrease and by how much?

2021-04-27
$$\displaystyle{h}={50}{\sin{{\left({6.0}\right)}}}={5.23}{m}$$
$$\displaystyle{m}{g}{h}=\frac{{1}}{{2}}{m}{v}^{{{2}}}$$
v = 10.1m/s
$$\displaystyle{m}_{{{c}}}\cdot{v}_{{{i}}}={m}_{{{f}}}\cdot{v}_{{{f}}}$$
$$\displaystyle{v}_{{{f}}}={m}_{{{c}}}\cdot\frac{{v}_{{{i}}}}{{m}_{{{f}}}}$$
$$\displaystyle{v}_{{{f}}}={6.97}\frac{{m}}{{s}}\cdot{5}{s}={34.8}$$ (they have enough time).
b) $$\displaystyle\frac{{1}}{{2}}{m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}=\frac{{1}}{{2}}\cdot{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}$$
$$\displaystyle\frac{{1}}{{2}}{\left({m}_{{{i}}}\cdot{{v}_{{{i}}}^{{{2}}}}-{m}_{{{f}}}\cdot{{v}_{{{f}}}^{{{2}}}}\right)}={4740}{J}$$
The kinetic energy decreased, this is to be expected with anon-elastic collision.