# A pilot of a downed airplane fires the emergency flare into the sky. The path of the flare is modeled by the equation h = 0.096(d-25)^2 +60, where his the hieght of the flare in metres when its...

A pilot of a downed airplane fires the emergency flare into the sky. The path of the flare is modeled by the equation h = 0.096(d-25)^2 +60, where his the hieght of the flare in metres when its horizontal distance from where it was propelled is d metres. An emergency helicopter equipped with special binoculars has a line of sight to the spot where the flare was launched. The line of sight from the binocular is modeled by the equation 9x-10y=-14.

a) Sovle the system and give answers rounded to two decimal places.

b) The line of sight from the binoculars spots the flare twice. How high was the flare closest to the ground when it as spotted the first time?

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### 1 Answer

`h=.096(d-25)^2+60,` where his the hieght of the flare in metres when its horizontal distance from where it was propelled is d metres.

Since horizontal distance represented by d and vertical distance by h, so we can write equation as

9d-10h=-14

9d+14=10h

(9d+14)/10=h (i)

Thus

`(9d+14)/10=.096(d-25)^2+60`

`9d+14=.96(d-25)^2+600`

`.96(d^2+625-50d)+600-9d-14=0`

`.96d^2+600-48d+600-9d-14=0`

`.96d^2-57d+1186=0`

`d=(57+-sqrt(3249-4554.24))/(2xx.96)`

`=(57+-36.13i)/(2xx.96)`

Horizontal distance d is imaginary, so vertical height will also imaginary.