For this case, the first thing we are going to do is write the generic equation of motion for the vertical axis.
We have then:
[tex]h = \frac {1} {2} gt ^ 2 + vo * t + h0[/tex]
Where,
For the first body:
[tex]h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21[/tex]
For the second body:
[tex]h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50[/tex]
By the time both bodies have the same height we have:
[tex]h1 = h2\\[/tex]
[tex]\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50[/tex]
Rewriting we have:
[tex]\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50[/tex]
[tex]\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21[/tex]
[tex]\frac {19} {12} * t = 29[/tex]
Clearing time:
[tex]t = 29 (\frac {12} {19})\\t = 18.31s[/tex]
Answer:
it takes 18.31s for the two window washers to reach the same height
Answer:
After 18.32 seconds two window washers will reach the same height.
Step-by-step explanation:
Let h is the height at which a window washer A meats other window washer B.
A is ascending with the speed = 8 inch per second
At present A is at the height = 21 ft or 21×12 inches = 252 inches
If they meet after time t then the equation representing this relation between height and time will be
h = 252 + 8t ---------(1)
Other window washer B is at height = 50 feet or 50×12 = 600 inch
B is coming down with the speed = 11 inches per second
After time t their height will be h = 600 - 11t --------(2)
Now equating both the equations
252 + 8t = 600 - 11t
8t + 11t + 252 = 600
19t = 600 - 252
19t = 348
t = [tex]\frac{348}{19}[/tex]
t = 18.32 seconds
