Gear Up for Dazzling Physics!

A homogeneous, right-angle-shaped body with mass $m,$ dimensions $a,$ and thickness $t \,(\ll a)$ slides along a smooth plane and impinges with its edge plastically against an obstacle $H.$

Calculate the minimum impact speed $v$ $($ in $\text{m/s})$ such that the body tilts over.

Assume that $m = 5\text{ kg}, a = 10 \text{ m},$ and $t = 1\text{ cm}.$