Question

In a Broadway performance, an 67.2-kg actor swings from a 3.20-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?

___ m

Answer 1

Velocity of the first actor ignoring air resistance
use energy equations

KE = PE
½mv² = mgh
v = √(2gh)

velocity immediately after picking up partner
use conservation of momentum

m1v1 + m2v2 = (m1 + m2)v3
as v2 is initially zero
m1v1 = (m1 + m2)v3
v3 = m1v1/(m1 + m2)

as v1 is our v from above

v3 = m1√(2gh)/(m1 + m2)

so

v3 = (67.2 kg) √(2(9.81)(3.20))/(67.2 + 55kg)
v3 = 4.355 m/s

which will also be their max speed during swinging.  

PE = KE
mgh = ½mv²
h = v² / 2g

h = 4.355² / 2(9.81)
h = 0.966 m