If we jumped a lot...

Classical Mechanics Level 2

Stand up. Jump. When you jump you give yourself a velocity away from the earth. If you have a mass of 80 kg and can jump 1 m high, what is the magnitude of the velocity in m/s you imparted to the earth when you left the ground?

Details and assumptions

  • Treat yourself as a point mass.
  • The mass of the earth is 6 × 1 0 24 6 \times 10^{24} kg.
  • The acceleration due to gravity is − 9.8 m / s 2 -9.8~m/s^2 .


The answer is 5.9E-23.

View wiki
David Mattingly by David Mattingly

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

David Mattingly Staff
May 13, 2014

If you jump one meter high, then the initial velocity you had when leaving the ground can be found via

v f 2 = v i 2 + 2 a y → 0 = v i 2 + 2 ( − 9.8 ) ( 1 ) → v i = 4.427 v_f^2=v_i^2+2ay\rightarrow 0=v_i^2+2(-9.8)(1)\rightarrow v_i=4.427 m/s.

By momentum conservation we therefore have m e v e = − m i v i m_e v_e=-m_i v_i which allows us to solve for the velocity of the earth, v e = − 5.9 E − 23 v_e=-5.9E-23 m/s. Taking the magnitude gives us our answer.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...