Collision inbound

(Everything is expressed in SI unit, i have omitted writing units.)

Let initial distance between A and C be $AC = k$ . This remains constant.

Now let velocity of C be $x$ and let the time when they meet be $t$ .

Assume that they meet at point H.

Thus, AH = 10t and CH = xt and AC=k

Applying cosine rule in triangle ACH,

$\cos 30^ \circ = \dfrac{k^{2} + 100t^{2}-(xt)^{2}}{10tk}$

Arranging a little bit, $t^{2}(100-x^{2}) -(10 \sqrt{3}k)t + k^{2} = 0$

Now since $t$ is real, the above equation's discriminant should be greater than or equal to 0.

$\implies 300k^{2}-400k^{2} + 4(xk)^{2} \geq 0$

$\implies \boxed{x \geq 5}$