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

Answer

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

    $v = \sqrt{2gh}$

    $v = \sqrt{2\times 9.8 \times 4.5}$ss

    $v = \sqrt{88.2}$

    $v =9.39\ m/s$

Using momentum conservation

momentum before collision = momentum after collision

 $MV = (M + m)v_f$

 $v_f= \dfrac{73.3 \times 9.39}{73.3+55}$

 $v_f= \dfrac{688.287}{128.3}$

 $v_f= 5.36\ m/s$

maximum height achieved

using energy conservation

$\dfrac{1}{2}mv_f^2 = m g h$

$h = \dfrac{v_f^2}{2g}$

$h = \dfrac{5.36^2}{2\times 9.8}$

h =1.465 m