Question

If a ball is thrown vertically upward from the roof of 64 foot building with a velocity of 64 ft/sec, its height after t seconds is s(t)=64+64t-16t^2.

A) What is the maximum height the ball reaches? (Solved: 128)
B) What is the velocity of the ball when it hits the ground (height 0)?

Answer 1

yes what is it that you asking for?

Answer 2

Sorry, it's my first time doing this and it posted before I wanted it to. I need to find the velocity of the ball when it hits the ground, but I'm not quite sure how to go about doing that.

Answer 3

when the ball hits the ground that mean s(t)=0

Answer 4

he the first part find the vertex like @Zale101 said

Answer 5

eek...

Answer 6

put 0 in for s(t) in the position function and solve for t. Then put that t in the velocity equation to find the velocity at height 0.

Answer 7

so you solved the first part
let's find the derivative at a point when the s(t)=0
we need to find at what instant t the ball hits the ground

Answer 8

If I put in 0 for s(t), would that mean plugging it into the quadratic formula? And then plugging that into 64-16t?

Answer 9

Nope solve s(t)=0
solve a quadratic equation

Answer 10

find t=?

Answer 11

t is 2

Answer 12

so you solve it? can i trust you on that answer?

Answer 13

Probably not

Answer 14

64+64t-16t^2=0 this is what you solved?

Answer 15

so?

Answer 16

Do I take the derivative of that and then solve it or do I do 64+64t-16t^2 = 0, change that the 4+4+t^2=0, subtract 8 from both sides, and then take the square root of 8?

Answer 17

nope solve a quadratic equation means
find the the zeros for that equation
the derivative step is coming later

Answer 18

and by the way it is 4+4t-t^2=0 not what you wrote

Answer 19

solve that

Answer 20

Okay, for the quadratic formula I go -0.828 and 4.828

Answer 21

did you use this one 4+4t-t^2=0?

Answer 22

no, i used the first one. should i have used that one?

Answer 23

which one did you call the first one
it's the same equatuon
64+64t-16t^2=0 is also 4+4t-t^2=0

Answer 24

64+64t-16t^2

Answer 25

that's the same as 4+4t-t^2=0

Answer 26

find the two solutions!

Answer 27

Okay, so I got 10.94 and -6.94

Answer 28

okay! you are positive with that?
if so then plug in that into the derivative of s(t)

Answer 29

which is the velocity

Answer 30

I got -111.04 but it still says I'm wrong? I think I must have missed something.

Answer 31

you didn't do it right
www.wolframalpha.com/input/?i=4%2B4x-x%5E2%3D0

Answer 32

you first things was right!

Answer 33

but i was not sure what equation you were using so i had to make sure
because you wrote 4+4t+t^2=0 which is not our equation

Answer 34

I plugged it into the derivative (64-16t)

Answer 35

x=4.8284

Answer 36

this is the value you have to plug in

Answer 37

your derivative is not correct

Answer 38

it should be s'(t)=64-32t

Answer 39

Oh shoot, sorry I completely missed that. I wrote over that in my notebook. Thanks so much for your help!

Answer 40

welcome^_^

Answer 41

alright i have to go

Answer 42

i think everything is clear now!

Answer 43

Yes it is! Thanks so much haha. I just completely missed what I wrote as the derivative because I had so much written in my notebook for this problem. Thanks for being patient!

Answer 44

No problem! good luck