His speed is exactly (350/27) miles per second ... about 46,667 mph. Wotta guy !
Well first of all, you must realize that it depends on how the jumpers are distributed on the earth's surface. If,say, one billion of them are in the eastern hemisphere and the other billion are in the western one, then the sum of all of their momenta could easily be zero, and have no effect at all on the planet. I'm pretty sure what you must have in mind is to consider the Earth to be a block, with a flat upper surface, and all the people jump in the same direction.
average mass per person = 60 kg.
jump velocity = 7 m/s straight up and away from the block, all in the same direction
one person's worth of momentum = (m) (v) = 420 kg.m/s
sum of two billion of them = 8.4 x 10¹¹ kg-m/s all in the same direction
Earth's "recoil" momentum = 8.4 x 10¹¹ in the opposite direction = (m) (v)
Divide each side by 'm' : v = (momentum) / (mass) =
The Earth's "recoil" velocity is (8.4 x 10¹¹) / (5.98 x 10²⁴) =
1.405 x 10⁻¹³ m/s =
<em> 0.00000000014 millimeter per second
</em>I have no intuitive feeling for this kind of thing, so can't judge whether
the answer is reasonable. But my math and physics felt OK on the
way to the solution, so that's my answer and I'm sticking to it.
During the fall, all the initial potential energy of the rock
has converted into kinetic energy of motion
where h is the initial height of the rock, m its mass, and v its velocity just before hitting the water. So, for energy conservation, we have
and so we can find the value of K, the kinetic energy of the rock just before hitting the ground:
Answer: -25.4
Explanation:
Acellus don’t forget the negative sign
