Question

A plane is descending into the airport. After 5 minutes it is at a height of 6500 feet. After 7 minutes it is at a height of 5900 feet. Write an equation to model its height after t minutes. When will it land assuming the airport is at 0 feet.

Answer 1

Let's assume

height of plane in feet =h

time in minutes =t

we are given

A plane is descending into the airport. After 5 minutes it is at a height of 6500 feet

so, we get one point as (5,6500)

After 7 minutes it is at a height of 5900 feet

so, we get another point as (7,5900)

we can use point slope form of line

`y-y_1=m(x-x_1)`

points as

(5,6500)

x1=5, y1=6500

(7,5900)

x2=7 , y2=5900

Calculation of slope(m):

`m=(y_2-y_1)/(x_2-x_1)`

now, we can plug values

`m=(5900-6500)/(7-5)`

`m=-300`

Equation of line:

we can use formula

`y-y_1=m(x-x_1)`

we can plug values

`h-6500=-300(t-5)`

`h=-300t+8000`

Time of landing:

we can set h=0

and then we can solve for t

`h=-300t+8000=0`

`t=(80)/(3)min`..............Answer