SOLUTION: The height h (in feet) of a rocket as a function of the time t (in seconds) of flight is given by the following equation. Determine the times t when the rocket is on the ground.

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Question 285567: The height h (in feet) of a rocket as a function of the time t (in seconds) of flight is given by the following equation. Determine the times t when the rocket is on the ground.
h=50+280t-16t(squared)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When t+=+0, the rocket is still on the ground, and
h+=+50 (height of rocket?)
The rocket is also on the ground when it comes
back down at h+=+0, so
-16t%5E2+%2B+280t+%2B+50+=+0
Using quadratic equation:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-16
b+=+280
c+=+50
t+=+%28-280+%2B-+sqrt%28+280%5E2-4%2A%28-16%29%2A50+%29%29%2F%282%2A%28-16%29%29+
t+=+%28-280+%2B-+sqrt%28+78400+%2B+64%2A50+%29%29%2F%28-32%29%29+
t+=+%28-280+%2B-+sqrt%28+78400+%2B+3200+%29%29%2F%28-32%29%29+
t+=+%28-280+%2B-+sqrt%28+81600+%29%29%2F%28-32%29%29+
t+=+%28-280+%2B-+285.657%29%2F%28-32%29%29+
The (+) square root gives me negative t,
so I can't use it
t+=+%28-565.657%29%2F%28-32%29%29+
t+=+17.677 sec
The rocket comes back to the ground in 17.677sec
Here's a plot of h vs t also:
+graph%28+500%2C+500%2C+-5%2C+22%2C+-50%2C+1300%2C+-16x%5E2+%2B+280x+%2B+50%29+