Actually Welcome to the concept of Efficiency.
Here we can see that, the Input work is given as 2.2 x 10^7 J and the efficiency is given as 22%
The efficiency is => 22% => 22/100.
so we get as,
E = W(output) /W(input)
hence, W(output) = E x W(input)
so we get as,
W(output) = (22/100) x 2.2 x 10^7
=> W(output) = 0.22 x 2.2 x 10^7 => 0.484 x 10^7
hence, W(output) = 4.84 x 10^6 J
The useful work done on the mass is 4.84 x 10^6 J
Complete part of Question: What is Jane's (and the vine's) angular speed just before she grabs Tarzan
Answer:
Jane's (and the vine's) angular speed just before she grabs Tarzan, w = 1.267 rad/s
Explanation:
According to the law of energy conservation:
Total change in kinetic energy = Total change in potential energy
Mass of Jane = 60 kg
Mass of the vine = 32 kg
Mass of Tarzan = 72 kg
Height of Tarzan = 5.50 m
Length of the vine = 8.50 m
Jane's change in gravitational potential energy,
Vine's gravitational potential energy,
Vine's Kinetic energy :
Jane's Kinetic energy:
3234 + 862.4 = 2167.5w² + 385.33w²
4096.4 = 2552.83w²
w² = 4096.4/2552.83
w² = 1.605
w = √1.605
w = 1.267 rad/s