anonymous
  • anonymous
A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t2 + 576t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit. i don't even understand what she is wanting me to do??????????
Mathematics
jamiebookeater
  • jamiebookeater
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goformit100
  • goformit100
How ois the Physics question posted here @.Sam.
amistre64
  • amistre64
math books have these types of questions as well
amistre64
  • amistre64
its asking you for the vertex of the parabola

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amistre64
  • amistre64
if you can find the roots, you can determine the t value as the middle of the roots
anonymous
  • anonymous
i Don't understand how to get to the vertex
amistre64
  • amistre64
|dw:1371055357886:dw|
amistre64
  • amistre64
can you find where the zeros for it are?
anonymous
  • anonymous
No
amistre64
  • amistre64
then you are clearly not prepared to tackle this problem.
amistre64
  • amistre64
can you factor the given equation?
anonymous
  • anonymous
yes i got to 16(t^2 + 36t)
amistre64
  • amistre64
pull out a t as well
anonymous
  • anonymous
16t(t+36) = 16t (t+6) (t-6)
amistre64
  • amistre64
16t (t+36) is as far as you can go now the key here is to remember your zero times tables ....
anonymous
  • anonymous
okay
amistre64
  • amistre64
16t (-t+36) = 0 when 16t=0, or when -t+36 = 0 what values do we get for "t"?
anonymous
  • anonymous
if 16t=0 then t is 0 and if -t+36=0 then -t=-36
amistre64
  • amistre64
good, so lets say it takes from t= 0 to 36 seconds to go up and come back down to the ground. (h=0) the great thing about a parabola is that it takes the same amount of time to go up as it does to go down. the highest point is therefore, half of the time interval. what is half way between 0 and 36 ?
anonymous
  • anonymous
18
amistre64
  • amistre64
good, then it takes 18 seconds for it to reach its maximum position, and another 18 seconds to fall back down to the ground
anonymous
  • anonymous
thank you :)
amistre64
  • amistre64
good luck :)
anonymous
  • anonymous
h(t)=-16t^2+576t \[\frac{ dh }{ dt }=-32t+576\] when it is at maximum height dh/dt =0 -32t+576=0,t=576/32=18 sec. when t=18 sec., h=-16*18*18+576=18(-16*18+32)=18*32(-9+1)=576*-8=-4608 maximum height reached=4608 units.

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