For this case, the we have that the generic equation of motion is:
We have then:
[tex]y = \frac {1} {2} gt ^ 2 + vo * t + yo[/tex]
Where,
First equation:
[tex]y1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21[/tex]
Second equation:
[tex]y2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50[/tex]
For same height we have:
[tex]y1 = y2\\[/tex]
[tex]\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50[/tex]
Clearing time:
[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]
[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:
18.32 seconds
Step-by-step explanation:
Given: one washer is 21 ft high rising 8 in per second. The other is 50 feet high descending 11inches per second.
To Find: Â How long does it take for the two window washers to reach the same height
Solution:
Initial height of first washer [tex]=21[/tex] [tex]\text{feets}[/tex]
               [tex]1\text{feet}=12\text{inch}[/tex]
height of first tower  [tex]=21\times12=252\text{inches}[/tex]
ascending rate of first tower[tex]=8[/tex] [tex]\text{in}/ \text{s}[/tex]
equation for height of first washer after [tex]\text{x}[/tex] seconds
                       [tex]=252+8\text{x}[/tex]
Initial height of second washer [tex]=50[/tex] [tex]\text{feets}[/tex]
                 [tex]1\text{feet}=12\text{inch}[/tex]
height of second tower  [tex]=50\times12=600\text{inches}[/tex]
descending rate of second tower[tex]=11[/tex] [tex]\text{in}/ \text{s}[/tex]
equation for height of second washer after [tex]\text{x}[/tex] seconds
                       [tex]=600-11\text{x}[/tex]
when height of both washers are equal
              [tex]252+8\text{x}=600-11\text{x}[/tex]
              [tex]19\text{x}=348[/tex]
              [tex]\text{x}=\frac{348}{19}[/tex]
              [tex]\text{x}=18.32\text{s}[/tex]
It will take 18.32s to both washers to reach the same height
