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 100 kg, and Ed has a mass of 81 kg. Following the push, Adolf swings upward to a height of 0.51 m above his starting point. To what height above his own starting point does Ed rise?

Answer 1

0.78 m

Step-by-step explanation:

By the conservation of energy, the energy that they gain from potential energy, must be equal to the kinetic energy. So, for Adolf:

Ep = Ek

ma*g*ha = ma*va²/2

Where ma is the mass of Adolf, g is the gravity acceleration (10 m/s²), ha is the height that he reached, and va is the velocity. So:

100*10*0.51 = 100*va²/2

50va² = 510

va² = 10.2

va = √10.2

va = 3.20 m/s

Before the push, both of them are in rest, so the momentum must be 0. The system is conservative, so the momentum after the push must be equal to the momentum before the push:

ma*va + me*ve = 0, where me and ve are the mass and velocity of Ed. So:

100*3.20 + 81ve = 0

81ve = 320

ve = 3.95 m/s

By the conservation of energy for Ed:

me*g*he = me*ve²/2

81*10*he = 81*(3.95)²/2

810he = 631.90

he = 0.78 m