Momentum Question: Initial Velocity of Earth & Why They Don't Move Away

[runningirl]

Homework Statement

You jump up, away from Earth. Is momentum conserved? With what initial velocity does the Earth recoil move away from you if your vertical displacement is 0.60 m? Why don't you and the Earth continue to move away from each other?

mass of Earth = 5.9742 × 1024 kilograms

Homework Equations

The Attempt at a Solution

i said that momentum would have to be conserved so... to find the initial velocity of the earth:

first find MY velociy:

.60=(vf^2)/2(9.8)

vf=3.42 m/s

5.9742 × 1024(vi)+m(0)=5.9742 × 1024(3.42)+110(3.42)

saying 110 is my mass...
but i wasn't sure if this was correct/what would be the Earth's "final velocity"?
would it have one?

 

[rock.freak667]

The Attempt at a Solution

i said that momentum would have to be conserved so... to find the initial velocity of the earth:

first find MY velociy:

.60=(vf^2)/2(9.8)

vf=3.42 m/s

This is correct.

5.9742 × 1024(vi)+m(0)=5.9742 × 1024(3.42)+110(3.42)

saying 110 is my mass...
but i wasn't sure if this was correct/what would be the Earth's "final velocity"?
would it have one?

I think you should assume that the initial velocity of the Earth is also zero. So your initial momentum is zero, and your final momentum will be 5.9742(10²⁴)v_f+110(3.42)

 

[runningirl]

This is correct.



I think you should assume that the initial velocity of the Earth is also zero. So your initial momentum is zero, and your final momentum will be 5.9742(10²⁴)v_f+110(3.42)

they were asking for Earth's initial velocity as it recoils away from me so it would just be 0?
also, how come Earth and i continue t move away from one another when i jump? is it because we exert the same force on one another but i have a higher acceleration than earth?

 

[rock.freak667]

they were asking for Earth's initial velocity as it recoils away from me so it would just be 0?
also, how come Earth and i continue t move away from one another when i jump? is it because we exert the same force on one another but i have a higher acceleration than earth?

You would need to solve 5.9742(10²⁴)v_f+110(3.42) = 0 for v_f.

You both exert an equal and opposite force on one another, the Earth just doesn't move since it is more massive than you.

 

[runningirl]

what would vf help me find?
would i use the kinematics equation:

.6=(vf^2-vo^2)/2(9.8)?

 

[rock.freak667]

what would vf help me find?
would i use the kinematics equation:

.6=(vf^2-vo^2)/2(9.8)?

You used that to get your final velocity when you jump off the surface.

in the consevervation of momentum equation

5.9742(10²⁴)v_fE+110(3.42) = 0

v_fE would be the final velocity of the Earth.

 

[runningirl]

but how would finding the Earth's final velocity help me find it's initial velocity?!

 

[rock.freak667]

but how would finding the Earth's final velocity help me find it's initial velocity?!

I think they want you to find the velocity the Earth move away from you due to the jump. Not the initial velocity before the jump.