Plane A is already at an altitude of 2172 feet.
Let this be called the "initial altitude" of plane A and be represented by [tex] H_{A}=2172 [/tex] feet
Likewise, the initial altitude of Plane B will be zero, because the plane B has just taken off from ground.
Thus, [tex] H_{B}=0 [/tex]
It is given that the altitude gaining speed of plane A is 35.25 feet/second.
Also, it is given that the altitude gaining speed of plane B is 80.5 feet/second.
Now, if at some point in time both the planes are at the same altitude, then obviously, the same amount of time, [tex] t [/tex], must have passed for both the planes.
Thus, altitude of plane A after those [tex] t [/tex] seconds will be:
[tex] H_{A}+35.25t [/tex].......................(Equation 1)
Likewise, the altitude of plane B after those [tex] t [/tex] seconds will be:
[tex] H_{B}+80.5t [/tex]..........................(Equation 2)
We know that after [tex] t [/tex] seconds, the altitude will be the same. Thus, our guiding equation will be:
[tex] H_{A}+35.25t=H_{B}+80.5t [/tex]
Which can be simplified to:
[tex] 2172+35.25t=80.5t [/tex]
[tex] 80.5t-35.25t=2172 [/tex]
[tex] 45.25t=2172 [/tex]
[tex] t=\frac{2172}{45.25} =48 [/tex]
Thus, 48 seconds will pass before the planes are at the same altitude.
The altitude of the planes when they are at the same altitude can be calculated by putting [tex] t=48 [/tex] in any of the two equations, (Equation 1) or (Equation 2).
Thus Altitude of the planes when they are at the same altitude, by using (Equation 1) is:
[tex] 2172+35.25\times 48=3864 [/tex] feet
We will get the same answer if we use (Equation 2).
Step-by-step explanation:
Plane A is already at an altitude of 2172 feet.
Let this be called the "initial altitude" of plane A and be represented by feet
Likewise, the initial altitude of Plane B will be zero, because the plane B has just taken off from ground.
Thus,
It is given that the altitude gaining speed of plane A is 35.25 feet/second.
Also, it is given that the altitude gaining speed of plane B is 80.5 feet/second.
Now, if at some point in time both the planes are at the same altitude, then obviously, the same amount of time, , must have passed for both the planes.
Thus, altitude of plane A after those seconds will be:
.......................(Equation 1)
Likewise, the altitude of plane B after those seconds will be:
..........................(Equation 2)
We know that after seconds, the altitude will be the same. Thus, our guiding equation will be:
Which can be simplified to:
Thus, 48 seconds will pass before the planes are at the same altitude.
The altitude of the planes when they are at the same altitude can be calculated by putting in any of the two equations, (Equation 1) or (Equation 2).
Thus Altitude of the planes when they are at the same altitude, by using (Equation 1) is:
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