This one reminds me of Zeno’s arrow paradox. Imagine that a meteor traveling in outer space enters a large cloud of inte
Posted: Sat Feb 26, 2022 11:50 am
This one reminds me of Zeno’s arrow paradox. Imagine that a
meteor traveling in outer space enters a large cloud of
interstellar hydrogen, and that the drag force exerted by the
hydrogen is proportional to the nth power of the meteor's velocity
so that F = −mβvn , where n is greater than 0. Assume the meteor
enters the cloud at t = 0, x = 0 with initial velocity v0. The
meteor never comes to rest, but does not necessarily escape to
infinity! For what values of n will the meteor have traveled a
finite distance after an infinite amount of time has passed? You
may find it convenient to rewrite m dv dt as m dv dx dx dt = mv dv
dx . This will let you work with an equation involving only x and v
rather than x, v, and t, and use it to solve for x as a function of
v.
meteor traveling in outer space enters a large cloud of
interstellar hydrogen, and that the drag force exerted by the
hydrogen is proportional to the nth power of the meteor's velocity
so that F = −mβvn , where n is greater than 0. Assume the meteor
enters the cloud at t = 0, x = 0 with initial velocity v0. The
meteor never comes to rest, but does not necessarily escape to
infinity! For what values of n will the meteor have traveled a
finite distance after an infinite amount of time has passed? You
may find it convenient to rewrite m dv dt as m dv dx dx dt = mv dv
dx . This will let you work with an equation involving only x and v
rather than x, v, and t, and use it to solve for x as a function of
v.