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rpmacs · Nov 21, 2009, 09:00 AM

A missile is fired vertically into the air. The distance s (in feet) above the ground as a function of time t (in seconds) is given by the equation below.
h=300+500t-16^2

(a) When will the missile hit the ground?
(b) When will the missile be 1000 feet above the ground?

Help!

Perito · Nov 21, 2009, 09:20 AM

Are you sure your equation isn't this:

$h = 300 + 500\,t - 16\,t^2$

a) When will the missile hit the ground?

I'm not sure if you're supposed to set h at 0 or h at 300. It appears, from the equation, that you start at 300 feet. The solution, however, is similar in either case.

... when h = 0

$0 = 300 + 500\,t - 16\,t^2$

solve for t. One root will be imaginary -- ignore that one.

... when h = 300

$0 = 500\,t - 16\,t^2$

One root is obviously 0 (time = 0; when the rocket is fired, it is fired from the ground). The second root will be when it crashes after flight.

b) When will the missile be 1000 feet above the ground?

... when h = 1000

$1000 = 300 + 500\,t - 16\,t^2$

$0 = -16\,t^2 + 500\,t - 700$

solve for t. You'll get two roots. One of the roots will tell you when the missile is 1000 feet from the ground and ascending; the other root will tell you when the missile is 1000 feet from the ground and descending. Both are correct answers.