Question

In a Broadway performance, an 78.0-kg actor swings from a R = 3.95-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

Mass of the actor M = 78.0 kg

Radius of swing R = 3.95 m

Linear velocity of actor V = (gR)^1/2 = (9.8x3.95)^1/2 = 6.222 m/s

Kinetic energy of actor K.E = MV²/2 = 78x6.222²/2 = 3019.38 J ................(1)

Mass of the costar m = 55.0 kg

The potential energy of both after picks up costar at height h is

P.E = (M+m)gh = (78+55)9.8xh = 1303.4h J -----------------(2)

But Kinetic energy of actor = The potential energy of both after picks up costar at height h

from (1), (2)

K.E = P.E

3019.38 = 1303.4h

h = 3019.38/1303 = 2.317 m