An asteroid is moving directly towards the centre of the earth....

$K{E}_{i} + P{E}_{i} = K{E}_{f} + P{E}_{f}$
$\dfrac{1}{2}m{u}_{0}^{2} + \left(- \dfrac{GMm}{10R}\right) = \dfrac{1}{2}m{v}^{2} + \left(- \dfrac{GMm}{R}\right)$
${v}^{2} = {u}_{0}^{2} + \dfrac{2GM}{R}\left[1 - \dfrac{1}{10}\right]$
$v = \sqrt{{u}_{0}^{2} + \left(\dfrac{9}{5}\right)\dfrac{GM}{R}}$

$= \sqrt{{12}^{2} + \left(\dfrac{9}{5}\right)\dfrac{{\left(11.2\right)}^{2}}{2}}$
$= \sqrt{144 + 0.9{\left(11.2\right)}^{2}} = \sqrt{156.896}$

$= 16.028km{s}^{- 1}$

$≃ 16km{s}^{- 1}$