## anonymous 3 years ago 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??????????

1. goformit100

How ois the Physics question posted here @.Sam.

2. amistre64

math books have these types of questions as well

3. amistre64

its asking you for the vertex of the parabola

4. amistre64

if you can find the roots, you can determine the t value as the middle of the roots

5. anonymous

i Don't understand how to get to the vertex

6. amistre64

|dw:1371055357886:dw|

7. amistre64

can you find where the zeros for it are?

8. anonymous

No

9. amistre64

then you are clearly not prepared to tackle this problem.

10. amistre64

can you factor the given equation?

11. anonymous

yes i got to 16(t^2 + 36t)

12. amistre64

pull out a t as well

13. anonymous

16t(t+36) = 16t (t+6) (t-6)

14. amistre64

16t (t+36) is as far as you can go now the key here is to remember your zero times tables ....

15. anonymous

okay

16. amistre64

16t (-t+36) = 0 when 16t=0, or when -t+36 = 0 what values do we get for "t"?

17. anonymous

if 16t=0 then t is 0 and if -t+36=0 then -t=-36

18. 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 ?

19. anonymous

18

20. 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

21. anonymous

thank you :)

22. amistre64

good luck :)

23. 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.