SOLUTION: A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even educational for physics and math, as this question il

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Question 1126994: A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even educational for physics and math, as this question illustrates. A potato launched by a particular potato gun has a height described by h(t)=-16t^2+120t+3. When is the potato 203 feet in the air?
The potato is 203 feet in the air after [blank] seconds on the way up and after [blank] seconds on the way back down.
** I first attempted to find the vertex and use it as my answer, which would have been (3.75,333).
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
203=-16t^2+120t+3
16t^2-120t+200=0
divide by 8
2t^2-15t+25=0
(2t-5)(t-5)=0
t=2.5 seconds and at 5 seconds
graph%28300%2C300%2C-6%2C7%2C-50%2C350%2C-16x%5E2%2B120x%2B3%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

h%28t%29=-16t%5E2%2B120t%2B3
When is the potato 203 feet in the air means h%28t%29=203
203=-16t%5E2%2B120t%2B3........solve or t; I am going to move all terms from the right to the left
16t%5E2-+120t%2B203-3=0
16t%5E2-+120t%2B200=0...factor out 8
8%282t%5E2-+15t%2B25%29=0....to factor rest, write -15t as -5t-10t
8%282t%5E2-+5t-10t%2B25%29=0.....group
8%28%282t%5E2-+5t%29-%2810t-25%29%29=0....actor out t from first group and 5 from second group
8%28t%282t-+5%29-5%282t-5%29%29=0
8+%28t+-+5%29+%282t+-+5%29+=+0
=> t=5%2F2=2.5s or t=5s
The potato is 203 feet in the air after 2.5 second on the way up and after 5+seconds on the way back down.