Question

I need to know how to work following problem: union motion- A small airplane approaches a runway at a speed of 90 miles per hour. When it is 1/2 Mike away, the plane is 200 feet above the level of the runway. What is the rate of decent of the plane, in feet per minute?

Answer 1

First lets convert everything to feet, and feet/min

1/2 mile = 5280/2 = 2640 feet
90 mi/hr = (90)(5280)/(60) = 7920 ft/min

Next lets find total distance plane is away from runway.
Set up right triangle where total distance is hypotenuse.
$d = \sqrt{200^2 + 2640^2} = 2647.5649$

Next we will use a little trig. Let theta be the angle of elevation from runway to the plane. The rate of descent is the vertical component of the planes speed. Find vertical component using sine.
$\frac{dy}{dt} = 7920 sin \theta$

Finally substitute ratio from right triangle for sin theta.
$\frac{dy}{dt} = 7920 (\frac{200}{2647.5649}) = 598.286$

The rate of descent is about 598 feet per minute.