Answer
14.97 m
Work Step by Step
Please see the attached image first.
According to the diagram we can say,
$x=\Delta R$
Let's apply the equation $S=ut+\frac{1}{2}at^{2}$ in the vertical direction to find the flight time of the stone 2 until it reach to the same horizontal level which it launch.
$\uparrow S=ut+\frac{1}{2}at^{2}$ ; Let's plug known values into this equation.
$0=13sin30^{\circ}m/s\times t+\frac{1}{2}(-9.8\space m/s^{2})t^{2}$
$t=1.33\space s$
Let's apply the equation $S=ut$ in the horizontal direction to find the x.
$\rightarrow S=ut$ ; Let's plug known values into this equation.
$x=13cos30^{\circ}\times1.33\space s=14.97\space m=\Delta R$
