Question

In a Broadway performance, an 73.3-kg actor swings from a 4.50-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

given,

mass of actor = 73.3 Kg

length of the cable = 4.5 m

mass of his costar = 55 Kg

maximum height they can reach =?

velocity just before colliding with costar

`v = √(2gh)`

`v = √(2* 9.8 * 4.5)`ss

`v = √(88.2)`

`v =9.39\ m/s`

Using momentum conservation

momentum before collision = momentum after collision

`MV = (M + m)v_f`

`v_f= (73.3 * 9.39)/(73.3+55)`

`v_f= (688.287)/(128.3)`

`v_f= 5.36\ m/s`

maximum height achieved

using energy conservation

`(1)/(2)mv_f^2 = m g h`

`h = (v_f^2)/(2g)`

`h = (5.36^2)/(2* 9.8)`

h =1.465 m