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 83.0 kg and your maximum jump height be 0.350 m. Model the Earth as a perfect

When you jump straight up, you give a small amount of recoil speed to the Earth. To calculate this, we need to use the conservation of momentum principle, which states that the total momentum of an isolated system remains constant. In this case, the system is you and the Earth. To find the recoil speed of the Earth, we can use the following equation: m1v1 + m2v2 = m1u1 + m2u2 Where m1 and m2 are the masses of you and the Earth respectively, v1 and v2 are your and the Earth's initial velocities, and u1 and u2 are your and the Earth's final velocities. Since you jump straight up, your initial velocity is zero. The Earth's initial velocity is also zero since we are modeling it as a perfectly solid object. Therefore, we can simplify the equation to: m2v2 = m2u2 Solving for u2, we get: u2 = v2 = (m1/m2) * sqrt(2gh) Where h is your maximum jump height and g is the gravitational acceleration, which is \approx imately 9.81 m/s^2. Plugging in the given values, we get: u2 = v2 = (83.0 kg / 5.97 x 10^24 kg) * sqrt(2 * 9.81 m/s^2 * 0.350 m) ? 6.12 x 10^-24 m/s So when you jump straight up as high as you can, you give a maximum recoil speed of \approx imately 6.12 x 10^-24 m/s to the Earth. This is an incredibly small amount and is negligible in comparison to the Earth's overall velocity.