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1 answer:
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Answer:
Time: 8 minutes
Altitude: 20000ft
Method 1 is easiest
Method 3 is easiest
Step-by-step explanation:
Given
Airplane 1:
Airplane 2:
Required
Determine when both planes would be at the same altitude?
Let the minute be represented by m
For Airplane 1, Its altitude at any height h is:
<em>It is minus (-) because the airplane is descending</em>
For Airplane 2, Its altitude at any height h is:
Method 1:
For both heights to be equal, we have that:
This gives:
Collect Like Terms
<em>Hence, the time they will be at the same altitude is 8 minutes</em>
Substitute 8 for m in
<em>Hence, they will be at the same altitude at 20000ft</em>
Method 2:
We have that:
Since they are to be at the same altitude, then
The difference in their altitude must be 0
i.e.
This gives
Collect Like Terms
Substitute 8 for m in
Method 3:
We have that:
Since they are to be at the same altitude, then
The ratio of their altitudes must be 1
i.e.
Cross Multiply
Collect Like Terms
Substitute 8 for m in
Hence;
<em>Their altitudes must be 20000ft</em>
<em>Though the three methods applied uses the same logic at some point, the first method applied is still the easiest and it is a straight forward method that could be applied in solving the question.</em>
<em>Method 3 is the most difficult.</em>