(Solved): A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends ...

A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (the figure). The waves are of two types: transverse waves traveling at \( v_{t}=64 \mathrm{~m} / \mathrm{s} \) and longitudinal waves traveling at \( v_{l}=155 \mathrm{~m} / \mathrm{s} \). If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference \( \Delta t \) in the arrival times of the waves at its leg nearest the beetle. If \( \Delta t=4.6 \mathrm{~ms} \), what is the beetle's distance?