A straight road passes through A. Point B is perpendicular distance d from the road, and its foot P is distance L along the road from A. A person moves on road at speed v and through field at speed v/n (n>1). He leaves road at C before P; let CP=x. The minimum-time condition is:
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Question

A straight road passes through A. Point B is perpendicular distance d from the road, and its foot P is distance L along the road from A. A person moves on road at speed v and through field at speed v/n (n>1). He leaves road at C before P; let CP=x. The minimum-time condition is:

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G1 Physics · Accepted Answer

T=(L−x)/v+n√(x²+d²)/v. Setting dT/dx=0 gives −1+nx/√(x²+d²)=0, hence x/√(x²+d²)=1/n.