Hi, I am struggling with finding the expected value for the following problem.

An infamous stretch of road stretching infinitely eastward from the origin over the interval [0, co) is known to be a hotspot for drag racing accidents. You are charged with placing a hospital at a location h along this semi-infinite stretch. If the location of an accident is governed by the unit exponential distribution, Exponential(1), what location of the hospital minimises the expected distance between the hospital and the accident? Determine this minimum expected distance