parametric equations

Question

An airplane at an altitude of 2000 feet is descending at a constant rate of 160 feet per second horizontally and 15 feet per second vertically.

a. write the pair of parametric equations that represent the airplane's flight path.

b. after how many seconds will the airplane touch down?

c. what horizontal distance will the airplane have traveled when it touches down on the runway?

Answer 1

Let x(t) and y(t) be distance horizontally and vertically respectively.

1) x(t) = 160t and y(t) = 2000 - 15t

2) the plane touches ground when y(t) =0

So, 2000 - 15t = 0

or 15t =2000

or t = 2000/15 = 133.33 seconds (approx)

3) The horizontal distance travelled by airplane when the plane touches the ground is

x(133.33) = 160*133.33 = 21333.32 feet (approx)