SOLUTION: If a model rocket is launched from the ground with an initial velocity of 288 feet per second. How long will it take to reach maximum height? Assume the parachute didn't open.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: If a model rocket is launched from the ground with an initial velocity of 288 feet per second. How long will it take to reach maximum height? Assume the parachute didn't open.      Log On


   

Question 970547: If a model rocket is launched from the ground with an initial velocity of 288 feet per second. How long will it take to reach maximum height?
Assume the parachute didn't open. How long would it take the rocket to return to earth?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think the equation is:
+h%28t%29+=+-16t%5E2+%2B+288t+
The +t+ coordinate of the maximum height
is at +t%5Bmax%5D+=+-b+%2F+%282a%29+
+a+=+-16+
+b+=+288+
+t%5Bmax%5D+=+-288+%2F+%282%2A%28-16%29%29+
+t%5Bmax%5D+=+288%2F32+
+t%5Bmax%5D+=+9+ sec
It will take 9 sec to reach maximum height
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When the rocket returns to earth, +h+=+0+
+0+=+-16t%5E2+%2B+288t+
+0+=+16t%2A%28+-t+%2B+18+%29+
+t+=+0+ ( the launch time )
+t+=+18+ ( return to earth )
In 18 sec the rocket returns to earth
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here's the plot:
+graph%28+400%2C+400%2C+-3%2C+24%2C+-150%2C+1500%2C+-16x%5E2+%2B+288x+%29+