## anonymous 5 years ago Arianna kicks a soccer ball off the ground and into the air with an initial velocity of 42 feet per second. Assume the starting height of the ball is 0 feet. Approximately what maximum height does the soccer ball reach?

1. anonymous

at wht angle to the ground is the ball kicked?

2. amistre64

the angle doesnt matter..... just gotta use the gravity formula... -16t o something

3. amistre64

asuume straight if anything :)

4. amistre64

striaght up... that is

5. anonymous

v=gt t=v/g=4.2seconds s=1/2gt^2=5*4.2^2=88.2feet

6. myininaya

http://www.purplemath.com/modules/quadprob.htm i think this site is helpful for writing formula for velocity

7. myininaya

or i mean height of the ball

8. myininaya

s(t)=-16t^2+42t+0

9. amistre64

s(t) = –G t^2 + V0(t) + H0 Vo = 42 ; H0 = 0; G = 16 s(t) = -16t^2 + 42t s'(t) = -32t + 42 = 0 at 42/32 = 21/16 = 1.3125

10. myininaya

s'(t)=-32t+42 s'(t)=0 when -32t+42=0 so t=42/32=21/16

11. myininaya

lol

12. amistre64

s(t) = -16(1.3125^2) + 42(1.3125) = 27.5625 :) maybe

13. myininaya

k i agree with amistre

14. amistre64

yay!!.... if great minds think alike; what does that leave for idiots lol

15. myininaya

we got something way different from that other guy

16. amistre64

he mighta used the 4.9 meters thing

17. myininaya

ok in this is in feet

18. myininaya

so maybe

19. anonymous

hello all. equation is $42t-16t^2$ max is when $t=\frac{-b}{2a}=\frac{21}{16}$ $42\times \frac{21}{16} -16\times(\frac{21}{16})^2=\frac{441}{16}$

20. myininaya

21. anonymous

;)

22. amistre64

yay!!! now if we can only determine that we are not a consensus of fools; I for one have my doubts since I am in it lol

23. anonymous

btw you have to use $h=h_0+v_0t-16t^2$ because you are working in feet. and you don't need calc to find the vertex of a parabola, although you can

24. amistre64

i did just casue I can :)

25. myininaya

right satelitle! derivatives are just more fun!

26. anonymous

i spose but after getting $\frac{-b}{2a}$for the 100th time maybe not.

27. myininaya

i like doing more math than i need to because its just fun lol

28. amistre64

more fun; less mechanical ;)

29. anonymous

on the other hand sometime it is silly to kill a fly with a grenade. you can get the vertex by simple algebra, completing the square or something.

30. myininaya

omg i would love to kill a fly with a grenade how is that not fun

31. anonymous

so not to be argumentative but i would not consider taking the derivative, setting to 0 and solving more or less mechanical than computing the vertex.

32. myininaya

lol ok you do that :)

33. myininaya

i might do it both ways just to show both ways and to do more MATH

34. anonymous

what i need to do is get back to my own work but somehow i keep coming here.

35. amistre64

i know right; it worse than cocaine in here lol