Hey!

A model rocket is launched. The height, in feet, of the rocket h(t) at t (t>=0) seconds after launch is determined by the equation h(t)= (-1/2)t^2 + 15t. The maximum height of the rocket is 112.5 feet.

(a) Find the number of seconds after launch it takes for the rocket to reach its maximum height. [Show all work]

(b) For how many seconds will the rocket be at a height of more than 100 ft? [Show all work]

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ok so its not like i tried it, i did, and let me show what i did.

first i plugged 112.5 for h(t) and got an answer of t=15 for part a.

for part b i plugged in 100 for h(t) and got 10 and 20. but i rejected 20 because thats higher than 15 which is the amount of time to reach the maximum height so that makes no sense. so i did 15 - 10 and got 5 for part b.

am i correct?