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There are three different ways to get from locationAto locationEin the diagram below. In path 1, you take an elevator directly from locationAstraight up to locationE. In path 2, you walk fromAtoB, climb a rope fromBtoC, then walk fromCtoE. In path 3, you walk from locationAtoD, then climb a ramp up to locationE. The following questions focus on the work done on a62kg person by the Earth while following each of these paths.

Taking the origin at locationA, the coordinates of the other locations are:_B=-3, 0, 0;_C=-3,20, 0;_D=48, 0, 0;_E> =0,20, 0.

(a) Path 1 (AtoE): What is the displacement vector%u0394for the path fromAtoEon the elevator? %u0394= ?????m

(b) What is the gravitational force acting on the person along path 1, as a vector? = ?????N

(c) What is the work done by the gravitational force of the Earth on the62kg person during the elevator ride fromAtoE? W₁=%u2022%u0394=J

(d) Path 2 (AtoBtoCtoE): What is the work done by the gravitational force of the Earth on the person as he walks fromAtoB? W_A%u2192B=J

(e) What is the work done by the gravitational force of the Earth on the person as he climbs fromBtoC? W_B%u2192C=J

(f) What is the work done by the gravitational force of the Earth on the person as he walks fromCtoE? W_C%u2192E=J

(g) What is the total work done by the gravitational force of the Earth on the person as the person goes fromAtoEalong path 2? W₂=J

(h) Path 3 (AtoDtoE): What is the work done by the gravitational force of the Earth on the person as he walks fromAtoD? W_A%u2192D=J

(i) What is the work done by the gravitational force of the Earth on the person as he climbs fromDtoE? W_D%u2192E=J

(j) What is the total work done by the gravitational force of the Earth on the person as the person goes fromAtoEalong path 3? W₃=J

(k) You calculated the work done by the gravitational force of the Earth on the person along three different paths. How do these quantities compare with each other?

W₁=W₂=W₃W₁W₂W₃W₃>W₁=W₂W₁>W₂>W₃