shortest distance question

Question

You’re lost in the woods, and your only hope of reaching civilization is to find your way back to the only road. You know you are exactly 1000 meters from the infinitely long, straight road. You have perfect relative bearings, are able to track your position perfectly, and can travel along any line or curve. You don't know the direction of the road and cannot see it until you are upon it. What is the shortest possible walking distance, to the nearest meter, that will ensure you reach the road?

Answer 1

Shubham, an approach might be to walk 1000 m in any direction, then turn exactly 90 degrees, walk in a circle of radius 1000 m, centered on your initial starting point. This will ensure that you reach the road. How long is this path?