Answer:
15 seconds.
Step-by-step explanation:
∵ The distance covered by plane in first second = 100 ft,
Also, in each succeeding second it climbs 100 feet more than it climbed during the previous second,
So, distance covered in second second = 200,
In third second = 300,
In fourth second = 400,
............, so on....
Thus, the total distance covered by plane in n seconds = 100 + 200 + 300 +400......... upto n seconds
( Sum of AP )
![=\frac{n}{2}(200+100n-100)](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bn%7D%7B2%7D%28200%2B100n-100%29)
![=\frac{n}{2}(100+100n)](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bn%7D%7B2%7D%28100%2B100n%29)
![=50n+50n^2](https://tex.z-dn.net/?f=%3D50n%2B50n%5E2)
Suppose the distance covered in n seconds is 12,000 feet,
![\implies 50n+50n^2=12000](https://tex.z-dn.net/?f=%5Cimplies%2050n%2B50n%5E2%3D12000)
![n+n^2=240](https://tex.z-dn.net/?f=n%2Bn%5E2%3D240)
![n^2+n-240=0](https://tex.z-dn.net/?f=n%5E2%2Bn-240%3D0)
![n^2+16n-15n-240=0](https://tex.z-dn.net/?f=n%5E2%2B16n-15n-240%3D0)
![n(n+16)-15(n+16)=0](https://tex.z-dn.net/?f=n%28n%2B16%29-15%28n%2B16%29%3D0)
![(n-15)(n+16)=0](https://tex.z-dn.net/?f=%28n-15%29%28n%2B16%29%3D0)
![\implies n=15\text{ or }n=-16](https://tex.z-dn.net/?f=%5Cimplies%20n%3D15%5Ctext%7B%20or%20%7Dn%3D-16)
∵ n can not be negative,
Hence, after 15 seconds the plane will reach an altitude of 12,000 feet above its takeoff height.