Question

In a Broadway performance, an 84.5-kg actor swings from a R = 4.30-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0-kg costar in an inelastic collision. What maximum height do they reach after their upward swing?

Answer 1

1.57772 m

Step-by-step explanation:

M = Mass of actor = 84.5 kg

m = Mass of costar = 55 kg

v = Velocity of costar

V = Velocity of actor

`h_i` = Intial height of actor = 4.3 m

g = Acceleration due to gravity = 9.81 m/s²

As the energy of the system is conserved

`(1)/(2)MV^2=Mgh_i\\\Rightarrow V=√(2gh_i)\\\Rightarrow V=√(2* 9.81* 4.3)\\\Rightarrow V=9.18509\ m/s`

As the linear momentum is conserved

`MV=(m+M)v\\\Rightarrow v=(MV)/(m+M)\\\Rightarrow V=(84.5* 9.18509)/(84.5+55)\\\Rightarrow v=5.56372\ m/s`

Applying conservation of energy again

`(1)/(2)(m+M)v^2=(m+M)gh_f\\\Rightarrow h_f=(v^2)/(2g)\\\Rightarrow h_f=(5.56372^2)/(2* 9.81)\\\Rightarrow h_f=1.57772\ m`

The maximum height they reach is 1.57772 m