Answer:
[tex]h = 2.821\,m[/tex]
Explanation:
The speed of the actor before the collision is found by means of the Principle of Energy Conservation:
[tex](83\,kg)\cdot(9.807\,\frac{m}{s})\cdot (3.90\,m) = \frac{1}{2}\cdot (83\,kg)\cdot v^{2}[/tex]
[tex]v = \sqrt{2\cdot (9.807\,\frac{m}{s^{2}} )\cdot (3.90\,m)}[/tex]
[tex]v \approx 8.746\,\frac{m}{s}[/tex]
The speed after the inelastic collision is obtained by using the Principle of Momentum Conservation:
[tex](83\,kg)\cdot (8.746\,\frac{m}{s} )+(55\,kg)\cdot (0\,\frac{m}{s} ) = (83\,kg + 55\,kg)\cdot v[/tex]
[tex]v = 5.260\,\frac{m}{s}[/tex]
Lastly, the maximum height is determined by using the Principle of Energy Conservation again:
[tex]\frac{1}{2}\cdot (138\,kg)\cdot (5.260\,\frac{m}{s} )^{2} = (138\,kg)\cdot (9.807\,\frac{m}{s^{2}} )\cdot h[/tex]
[tex]h = \frac{(5.260\,\frac{m}{s} )^{2}}{9.807\,\frac{m}{s^{2}} }[/tex]
[tex]h = 2.821\,m[/tex]
