Question

In a Broadway performance, an 84.5-kg actor swings from a R = 4.25-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

Velocity of the first actor ignoring air resistance we use conservation of energy equations
KE = PE
½mv² = mgh


To calculate velocity immediately after picking up partner :
We use conservation of momentum

as v₂ is initially zero



as v1 is our v from above we calculate

v₃ = m₁√(2gh)/(m₁ + m₂)
so we get:
v₃ = 84.5√(2(9.81)(4.25))/(84.5 + 55)
v₃ = 5.53 m/s

which will also be their max speed during swinging.

Now to calculate the maximum height reached, we use conservation of energy theorem again:

PE = KE
mgh = ½mv²
h = v² / 2g

h = 5.53² / 2(9.81)
h = 1.56 m