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?

- anonymous

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- anonymous

at wht angle to the ground is the ball kicked?

- amistre64

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

- amistre64

asuume straight if anything :)

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## More answers

- amistre64

striaght up... that is

- anonymous

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

- myininaya

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

- myininaya

or i mean height of the ball

- myininaya

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

- 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

- myininaya

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

- myininaya

lol

- amistre64

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

- myininaya

k i agree with amistre

- amistre64

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

- myininaya

we got something way different from that other guy

- amistre64

he mighta used the 4.9 meters thing

- myininaya

ok in this is in feet

- myininaya

so maybe

- anonymous

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

- myininaya

we already win :)

- anonymous

;)

- 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

- 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

- amistre64

i did just casue I can :)

- myininaya

right satelitle! derivatives are just more fun!

- anonymous

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

- myininaya

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

- amistre64

more fun; less mechanical ;)

- 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.

- myininaya

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

- 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.

- myininaya

lol ok you do that :)

- myininaya

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

- anonymous

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

- amistre64

i know right; it worse than cocaine in here lol

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