Question

Suppose all the people of the Earth go to the North Pole and, on a signal, all jump straight up. Estimate the recoil speed of the Earth. The mass of the Earth is 6 1024 kg, and there are about 6 billion people (6 109). Take the average mass of a person to be 74 kg and the distance the average person's center of mass rises after leaving the ground to be 0.2 m. m/s Additional Materials

Answer 1

Explanation:

It is known that relation between velocity and height is as follows.

              v = $\sqrt{2gh}$

where,     g = acceleration due to gravity = 9.8 $m/s^{2}$

                h = height = 0.2 m

Therefore, velocity is calculated as follows.

            v = $\sqrt{2gh}$

               = $\sqrt{2 \times 9.8 \times 0.2}$

               = 3.92 m/s

Also,

      $m_{people}v_{people} = m_{earth}v_{earth}$

    $v_{earth} = \frac{m_{people}v_{people}}{m_{earth}}$

Putting the given values into the above formula as follows.

     $v_{earth} = \frac{m_{people}v_{people}}{m_{earth}}$

                = $\frac{6 \times 10^{9} \times 74 kg/person}{6 \times 10^{24} kg}$

                = $\frac{444 \times 10^{9}}{6 \times 10^{24}}$

                = $74 \times 10^{-15}$ m/s

or,             = $7.4 \times 10^{-14}$ m/s

Thus, we can conclude that recoil speed of the Earth is $7.4 \times 10^{-14}$ m/s.