A man in a car at Q on a straight highway moves with speed u. He wants to reach point P in a field at perpendicular distance d from the highway. His speed in the field is u/2. In the figure, what should RM be so that total travel time to P is minimum?

Question

G1 Physics · Accepted Answer

Let x=RM. Highway distance differs by -x, while field distance is √(x²+d²) travelled at speed u/2. Ignoring constants, total time ∝-x+2√(x²+d²). Set derivative zero: -1+2x/√(x²+d²)=0 ⇒ 4x²=x²+d² ⇒ x=d/√3. Hence option B.