How fast can you set the Earth moving? In particular, when you jump straight up as high as you can, what is the maximum recoil speed that you give to the Earth? Let your mass be 84.0 kg and your maximum jump height be 0.500 m. Model the Earth as a perfectly solid object.
please help. :-)How fast can you set the Earth moving? In particular, when you jump straight up as high as you can, what is...?
Well the force you exert is what the Earth will feel. Newton's Laws. Every action has an equal and opposite reaction. So it is a question of momentum.
a = acceleration
g = accleration due ot gravity
m = mass
h = height
m you = 84 kg
m earth = 5.96 脳 10^24 kg
you have to overcome gravity and that is h = 0.5 g t^2
t = (2 h g)^0.5 = 3.13 s
v = g t = 9.81 x 3.13 = 30.70 m/s
Conservation of momentum
m1v1 = m2v2
v2 = m1v1 / m2 = 84 x 30.7 / 5.96 脳 10^24
v2 = 482 x 10^-24 m/s = 4.82 x 10^-22 m/s
