A projectile is fired straight up from ground level. After t seconds it's height is above the ground is h feet where h=-16t^2+144t. For what time period is the projectile at least 288 ft off the ground?

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A projectile is fired straight up from ground level. After t seconds it's height is above the ground is h feet where h=-16t^2+144t. For what time period is the projectile at least 288 ft off the ground?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Plug in 288 for h, move it over to the right side and do the quadratic formula to solve for t. You will get 2 times, in between and including those times will give you the period it is at least 288 ft off the ground.
so you end up with an equation like this 0=-16t^2+144t-288??
hi radar.

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Other answers:

You can simplify this and not need to use the quadratic. \[288=-16t ^{2}+144t\] Divide through by 16 getting 18=-t^2 + 9t
so you end up with 3 and 6?
\[t ^{2}-9t+18=0\] Is what you would get after rearranging the equation Now you have something you can easily factor. Hi Raslk2kl1
Yes now I don't know if that means it was above 288 feet for the time 3 thru 6 seconds or not. can you figure that out
Yes, the way I enter the answers seems like it is between 3 and 6 seconds
Fine, good luck.

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