SOLUTION: Hi, I need help with this word problem if someone could help me i would greatly appreciate it. A fireworks shell is shot straight up with an initial velocity of 120 feet per se

Question 878045: Hi, I need help with this word problem if someone could help me i would greatly appreciate it.
A fireworks shell is shot straight up with an initial velocity of 120 feet per second. Its height s in feet after t seconds is approximated by the equations s=120t-16t^2. if the shell is designed to explode when it reaches its maximum height, how long after being fired, and at what height, will the fireworks appear in the sky?
thank you for your time.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
s = 120t-16t^2
this is an equation for a parabola that opens downward
the time t where it changes direction is -b/2a, therefore
t = -(120) / 2(-16) = 120/32 = 3.75 seconds
the height s is
s = 120(3.75) - 16(3.75)^2 = 435.9375 feet
therefore in 3.75 seconds the fireworks will explode at at height of 436 feet

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