Mathematics
Mathematics
Problem
A vertical cliff is 30 m high. A platform juts horizontally 6 m out from the cliff face and is 10 m below the top. A rescue rope is to run in two straight segments: one from the top of the cliff to the outer edge of the platform, and the second from that edge to a point on the ground 40 m horizontally from the foot of the cliff. To the nearest tenth of a metre, what is the minimum total length of rope required? a) b) c) d)Intuitive explanation
This is an optimization problem where you need to find the position of the platform's outer edge that minimizes total rope length. The key insight is that the outer edge position is fixed at 6 m from the cliff and 10 m below the top, so you're really just calculating the two rope segments using the Pythagorean theorem and adding them. Set up a coordinate system with the cliff base at the origin, then use the distance formula to find each segment's length and sum them.
Intuitive explanation
This is an optimization problem where you need to find the position of the platform's outer edge that minimizes total rope length. The key insight is that the outer edge position is fixed at 6 m from the cliff and 10 m below the top, so you're really just calculating the two rope segments using the Pythagorean theorem and adding them. Set up a coordinate system with the cliff base at the origin, then use the distance formula to find each segment's length and sum them.