>>7626061I liked this problem anon. You basically have the right idea; it needs to be tweaked though.
The farthest you can reach on the y-axis road is the distance y=s*(1 sec). If you travel along the road for time t < 1 sec, reaching the point x=0, y=s*t, then go off-road in any other direction, you have (1-t) seconds left to travel at 1 unit/sec. Therefore the region you can reach consists of the family of circles
The two lines
are tangent to all these circles at the points
and they cross at y-intercepts (0,s).
So the region you want is bounded below (and to the sides) by the circle (for t=0)
And above by those two lines. These lines are tangent to the circle (t=0) at
The region has the inverted-ice-cream-cone shape. See pic related.
