Question

Adolf and Ed are wearing harnesses and are hanging at rest from the ceiling by means of ropes attached to them. Face to face, they push off against one another. Adolf has a mass of 120 kg, and Ed has a mass of 70 kg. Following the push, Adolf swings upward to a height of 0.52 m above his starting point. To what height above his own starting point does Ed rise?

Answer 1

Explanation:

It is given that,

Mass of Adolf, $m_1=120\ kg$

Mass of Ed, $m_2=70\ kg$

Adolf swings upward to a height of 0.52 m above his starting point. Initially both men are at rest. Their momentum will remain conserved.

Firstly, finding the speed of Adolf by using the conservation of energy as :

$mgh=\dfrac{1}{2}mv^2$

$v=\sqrt{2gh}$

$v=\sqrt{2\times 9.8\times 0.52}$

v = 3.19 m/s

Let v' is the speed of Ed. It can be calculated using the conservation of momentum as :

$m_1v+m_2v'=0$

$v'=-\dfrac{m_1v}{m_2}$

$v'=-\dfrac{120\times 3.19}{70}$

v' = -5.46 m/s

Let H is the height above which Ed rise. It can be calculated using the conservation of energy again as:

$H=\dfrac{v^2}{2g}$

$H=\dfrac{(-5.46)^2}{2\times 9.8}$

H = 1.52 meters

So, Ed will rise to a height of 1.52 meters. Hence, this is the required solution.