two people are wearing harnesses and are hanging from the ceiling by means of ropes. they are face to face and push off eachother. person 1 has a mass of 100kg and person 2 a mass of 80 kg. after the push person 1 swings in an arc that causes hime to rise a height of .3 meters. what height does person 2 rise above his starting position?
both have the same momentum at pushing
80v2=100v1
v2=1.25v1
square it
v2^2=1.56v1^2
so,
so the energy in person1 is m1v1^2
and the energy in person1 is m2v2^2
but m2*g*h2=1/2 m2v2^2=1/2 m2*1.56v1^2
= 1/2*4/5m1v1^2*1.56
= initialKEperson1 * .8*1/56
= m1g*h1*1.25
h2/h1=m1/m2*1.25
=1.25^2=1.56
or h2= 3*1.56meters
check my thinking.
To determine the height to which person 2 rises above their starting position, we can use the principle of conservation of momentum.
The principle states that the total momentum before the push is equal to the total momentum after the push. Since there is no external force acting on the system, the momentum remains constant.
Let's denote the initial velocity of person 1 as v1i, the initial velocity of person 2 as v2i, the final velocity of person 1 as v1f, and the final velocity of person 2 as v2f. The masses of person 1 and person 2 are given as 100 kg and 80 kg, respectively.
Before the push, the momentum is given by:
Initial momentum = (mass of person 1 * velocity of person 1) + (mass of person 2 * velocity of person 2)
Initial momentum = (100 kg * v1i) + (80 kg * v2i)
After the push, the momentum is given by:
Final momentum = (mass of person 1 * velocity of person 1) + (mass of person 2 * velocity of person 2)
Final momentum = (100 kg * v1f) + (80 kg * v2f)
According to the conservation of momentum, the initial momentum should be equal to the final momentum:
Initial momentum = Final momentum
(100 kg * v1i) + (80 kg * v2i) = (100 kg * v1f) + (80 kg * v2f) ---(Equation 1)
Next, we need to consider the conservation of energy. When person 1 swings in an arc and rises a height of 0.3 meters, they gain potential energy. This energy must come from the energy transferred during the push. Since potential energy is given by mass times gravity times height, the change in potential energy for person 1 is:
Potential energy gain for person 1 = (mass of person 1 * gravity * height)
Potential energy gain for person 1 = (100 kg * 9.8 m/s^2 * 0.3 m) ---(Equation 2)
Since person 2 is initially at the same height as person 1, the potential energy gain for person 2 will be the same as person 1.
Now, we can equate the gain in potential energy to the work done during the push, which is equal to the change in kinetic energy:
Potential energy gain for person 1 + Potential energy gain for person 2 = Work done during the push
(100 kg * 9.8 m/s^2 * 0.3 m) + (80 kg * 9.8 m/s^2 * height of person 2) = (1/2 * 100 kg * v1f^2) + (1/2 * 80 kg * v2f^2)
From here, you can solve the equation to find the final velocity of person 2 (v2f), and then use the final velocity to calculate the height that person 2 rises above their starting position using the equation for potential energy.
However, please note that without knowing the specific values for the height of person 2 or the initial velocities of both persons, we cannot provide an exact numerical answer to the question.