#### Question

Adolf and Ed are wearing harnesses and are hanging from the ceiling by means of ropes attached to them. They are face to face and push off against one another. Adolf has a mass of 116 kg, and Ed has a mass of 70 kg. Following the push, Adolf swings upward to a height of 0.65 m above his starting point. To what height above his starting point does Ed rise?

conservation of momentum tells us that M1 = M2

conservation of energy tells us that E1 = E2

Let's calculate the energy needed to move Adolf to his final state (0.65 m above starting point).

E2 = m * g * h

= 116 kg * 9.81 m/s^2 * 0.65 m

=739.7 J

That means that he started with that much energy as soon as he pushed off.

E1 = 1/2 * m * v^2

739.7 J = 1/2 * 116 kg * v^2

Solve for v, which turns out to be 3.6 m/s.

Now let's turn to momentum (calling M1 for Adolf and M2 for Ed)

M1 = M2

m1 * v1 = m2 * v2

116 kg * 3.6 m/s = 70 kg * v2

Solve for Ed's initial speed, v2 = 6.0 m/s

Now, using energy, let's find out Ed's final height.

E3 = E4 (now doing conservation of energy for Ed)

1/2 * m * v^2 = m * g * h

1/2 * 70 kg * (6.0 m/s)^2 = 70 kg * 9.81 m/s^2 * h

Solve for h, which ends up being h = 1.83 m above his starting point.

Let me know if this helps by choosing this as the best answer.

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