Answer:
it moves 25 inches.
Explanation:
the east west bit isn't important, ignore it. if an ant starts at 6 then moves to 19 then we need to subtract 19 from 6, that's 13. then it moves to 7. the difference between 19 and 7 is 12. add that to 13 and you get 25. it's important to remember that there is no such thing as negative distance. if it moved, then it counts.
Explanation:
It is given that,
Force, 
Position vector, 
(a) The torque on the particle about the origin is given by :
(b) To find the angle between r and F use dot product formula as :
Hence, this is the required solution.
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.
