Answer:
1.57772 m
Explanation:
M = Mass of actor = 84.5 kg
m = Mass of costar = 55 kg
v = Velocity of costar
V = Velocity of actor
[tex]h_i[/tex] = Intial height of actor = 4.3 m
g = Acceleration due to gravity = 9.81 m/s²
As the energy of the system is conserved
[tex]\frac{1}{2}MV^2=Mgh_i\\\Rightarrow V=\sqrt{2gh_i}\\\Rightarrow V=\sqrt{2\times 9.81\times 4.3}\\\Rightarrow V=9.18509\ m/s[/tex]
As the linear momentum is conserved
[tex]MV=(m+M)v\\\Rightarrow v=\frac{MV}{m+M}\\\Rightarrow V=\frac{84.5\times 9.18509}{84.5+55}\\\Rightarrow v=5.56372\ m/s[/tex]
Applying conservation of energy again
[tex]\frac{1}{2}(m+M)v^2=(m+M)gh_f\\\Rightarrow h_f=\frac{v^2}{2g}\\\Rightarrow h_f=\frac{5.56372^2}{2\times 9.81}\\\Rightarrow h_f=1.57772\ m[/tex]
The maximum height they reach is 1.57772 m
