Two research probes are dropped from rest at different altitudes during a planetary landing simulation. Probe $P_1$ is released from an altitude of $A$ metres. Probe $P_2$ is released $\delta$ seconds after $P_1$ from an altitude of $rA$, where $r$ is a constant such that $0<r<1$. Both probes reach the surface at the same time, exactly 6 seconds after the release of $P_1$. Assuming the probes move under constant acceleration due to gravity $g$ and air resistance is ignored,