A meteorite travelling through space enters a cloud of gas. The initial speed is $u$ , and after penetrating the cloud by a distance of $x$ the deceleration is $kx^2$ . Find the distance the meteorite penetrates?

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Answer 1 · 2018-06-17T10:18:54

$a = v (dv)/(dx) = - k x^2$

Separating and integrating:

$int_u^(v(x)) v \ d v = - k int_0^x \ x^2 \ dx$

$v^2/2 - u^2/2= - k/3 x^3$

Upon meteorite coming to rest:

$implies bb( x = root3((3 u^2)/(2k)) )$

A meteorite travelling through space enters a cloud of gas. The initial speed is uu , and after penetrating the cloud by a distance of xx the deceleration is kx^2kx^2 . Find the distance the meteorite penetrates?