Question

Why does the rider fall in the forward direction when a running horse stops suddenly

Answer 1

it is due to the inertia of motion... the rider body wants to be in motion even when the horse stops. so, as a result, the rider falls down when the horse stops suddenly.

Answer 2

it is because of inertia of motion when the horse stops suddenly the lower body part of the Rider stops with the horse but the upper body part remains in motion so tend to fall forward