## AValderrama16 Group Title 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?????????? one year ago one year ago

1. goformit100 Group Title

How ois the Physics question posted here @.Sam.

2. amistre64 Group Title

math books have these types of questions as well

3. amistre64 Group Title

its asking you for the vertex of the parabola

4. amistre64 Group Title

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

5. AValderrama16 Group Title

i Don't understand how to get to the vertex

6. amistre64 Group Title

|dw:1371055357886:dw|

7. amistre64 Group Title

can you find where the zeros for it are?

8. AValderrama16 Group Title

No

9. amistre64 Group Title

then you are clearly not prepared to tackle this problem.

10. amistre64 Group Title

can you factor the given equation?

11. AValderrama16 Group Title

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

12. amistre64 Group Title

pull out a t as well

13. AValderrama16 Group Title

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

14. amistre64 Group Title

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

15. AValderrama16 Group Title

okay

16. amistre64 Group Title

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

17. AValderrama16 Group Title

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

18. amistre64 Group Title

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. AValderrama16 Group Title

18

20. amistre64 Group Title

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. AValderrama16 Group Title

thank you :)

22. amistre64 Group Title

good luck :)

23. surjithayer Group Title

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.