Respuesta :
Answer:
[tex]t = 2\ s[/tex]
Explanation:
given,
length of the rope = 16 m
speed of the man = 2 m/s
using the formula of time period
[tex]T =2 \pi \sqrt{\dfrac{L}{g}}[/tex]
[tex]T =2 \pi \sqrt{\dfrac{16}{9.8}}[/tex]
[tex]T = 8.028\ s[/tex]
To cover the maximum distance you need to leave the when the rope is shows maximum displacement.
To reach the displacement time to leave the rope is one fourth of the time period.
[tex]t = \dfrac{T}{4}[/tex]
[tex]t = \dfrac{8.03}{4}[/tex]
[tex]t = 2\ s[/tex]
The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.
The total time taken to hang on if you want to drop into the water at the greatest possible distance from the edge is 2 seconds.
What is time period of pendulum?
The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.
It can be given as,
[tex]T=2\pi\sqrt{\dfrac{T}{g}}[/tex]
Here, [tex]g[/tex] is the gravitational force of Earth.
Given information-
Total length of the rope is 16 m.
The speed of the man is 2.0 m/s.
Let the time of to swing by rope both side is [tex]T[/tex]. Thus put the values in the above formula as,
[tex]T=2\pi\sqrt{\dfrac{16}{9.8}}[/tex]
[tex]T=8.028 \rm s[/tex]
Now the greatest possible distance from the edge will be at the greatest displacement.
Thus the time to cove the greatest possible distance will be one forth (1/4) of the total time. Thus,
[tex]t=\dfrac{8.028 }{4}\\t=2\rm s[/tex]
Hence, the total time taken to hang on if you want to drop into the water at the greatest possible distance from the edge is 2 seconds.
Learn more about the time period of pendulum here;
https://brainly.com/question/3551146
