Answer
$2.45\times 10^8m/s$
Work Step by Step
We can find the required speed of the ship as follows:
$\Delta t=\frac{\Delta t_{\circ}}{\sqrt{1-v^2/c^2}}$
We know that
$v=\frac{d}{\Delta t}$
$\implies v=\frac{d}{\Delta t_{\circ}}\sqrt{1-v^2/c^2}$
After Squaring both sides and simplifying the above equation, we obtain:
$d^2=v^2(\Delta t_{\circ}^2+d^2/c^2)$
This simplifies to:
$v=\frac{d}{\sqrt{\Delta t_{\circ}^2+d^2/c^2}}$
We plug in the known values to obtain:
$v=\frac{4.24\times 10^8}{\sqrt{(1.00)^2+(4.24\times 10^8)^2/(3.00\times 10^8)^2}}$
$v=2.45\times 10^8m/s$
