Choosing a sample rate and anti-aliasing for an IMU

You are streaming data from an accelerometer on a mobile robot. The motion you care about is below $20\,\text{Hz}$, but the sensor also picks up structural and motor vibration with significant energy near $300\,\text{Hz}$. A colleague proposes sampling at $50\,\text{Hz}$ and applying a digital low-pass filter in software to remove the vibration.

Explain what is wrong with this plan. Cover: (a) what the Nyquist criterion says about the $50\,\text{Hz}$ choice given the $300\,\text{Hz}$ content, (b) what specifically happens to that $300\,\text{Hz}$ energy after sampling and why a software low-pass filter cannot fix it, and (c) what you would change in the signal chain to do this correctly.