Question

A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 40 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 80 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked: 10 feet? Answer = 30 feet? Answer =

Answer 1

Answer:0.246ft/s

Step-by-step explanation: when the the worker starts moving and stops 10 feets away from lateral rope connecting the load, it forms a right angle triangle as see in the pix.

V = s/t ... equ 1

S= distance traveled by worker while pulling the rope = 10 ft

V = velocity of worker = 2ft/s

T = time taken the worker to move 10 ft = time taken for the load to move up = 5seconds

Use Pythagoras theorem to determine distance from pulley to new position of worker

Square root of (40^2 + 10^2) = 41.23ft

Distance traveled by load = D = 41.23 - 40

=1.23ft

Speed of load = D/ t...equ2

Substituting D and the into equ2

S.l = speed of load = 1.23/5 =0.246ft/s