Question

WHO IS GOOD IN CALC THAT CAN HELP ME FOR A FAN AND MEDAL!!!???

Answer 1

\[a = -32 \]

Answer 2

\[v = \int\limits_{}^{}a(t)dt + c\]

Answer 3

to find c, you must plug in the known values: v(0) = 40

Answer 4

now find the time t, the ball will hit the ground which is when the position function is 0.

Answer 5

\[s(t) = 500 + \int\limits_{}^{}vdt\]

Answer 6

once you find the t, time, in which the ball will hit the ground, plug it into v and you got your answer

Answer 7

sorry i got disconnected!!

Answer 8

wait, ah im confused

Answer 9

can we do this step by step?

Answer 10

yes. first find the velocity function

Answer 11

how do i do that if all i know is a..

Answer 12

the anti derivative of a is your v

Answer 13

in other words, the integral of a is your v

Answer 14

so now youre saying to get the integral of my a? im so confused

Answer 15

integral = anti derivative. yes.

Answer 16

am i still confusing you?

Answer 17

oh now i got it

Answer 18

im getting no solution..

Answer 19

great. so once you get your v, you will have a c in your equation. to find out what c is, remember that v(0) = 40

Answer 20

oh not great :( umm so here

Answer 21

\[v = \int\limits_{}^{} a(t) dt + c\]

Answer 22

a(t) = 32 ft/s^2

Answer 23

what is the integral of a constant, 32?

Answer 24

-32*

Answer 25

-32x+c

Answer 26

great! so v = -32x + c

Answer 27

now you need to find c, which will be easy given that v(0) = 40

Answer 28

what is c?

Answer 29

in my case, i've been using t instead of x. so try replacing my t with x if thats what has been confusing you

Answer 30

wait so i plug in now?..

Answer 31

did you find the velocity function

Answer 32

yes i thought that was v=-32x+C

Answer 33

yes but now you need to find C.

Answer 34

we were given that at the start of the throw (x=0), the velocity was 40ft/sec

Answer 35

so to find see we must do this:

v(0) = 40 = -32(0) + C

C= ?

Answer 36

0

Answer 37

i get confused when it is written out ahha

Answer 38

i dont think i get what youre trying to say

Answer 39

sorry math is my worst subject, but once i get it i understand it very well

Answer 40

Sry i just blindly said that C was 0 earlier at this point. It is NOT 0. Look at the equation again

Answer 41

40 = -32(0) + C

What is C?

Answer 42

C is 40. So the real complete velocity function is V(x) = -32x + 40

Answer 43

C=40

Answer 44

Now we will find the position function

S = integral of v(x)

S= -16x^2 + 40x + C

Answer 45

We will now solve for C for the position function
Given : S(0) = 500
500 = -16x^2 + 40x + C

Answer 46

500 = -16(0)^2 + 40(0) + C
C= 500

Answer 47

S(x) = -16x^2 + 40x + 500

Answer 48

To find when the object hits the ground, make s(x) = 0

Solve for x

Answer 49

so its 500?

Answer 50

No

Answer 51

Solve for x :

0 = -16x^2 + 40x + 500

Answer 52

oh i thought x is 0 sorry!

Answer 53

wait there are 2 x's, which one?

Answer 54

The one that makes the most sense. if its negative, obviously do not use it as a negative time doesn't exist

Answer 55

16x^2-500/40=x

Answer 56

No.

Answer 57

use the quadratic formula or your calculator to solve for the x's

Answer 58

i need to go do my own homework. winter break is over LOL so i got lots. I'm not interested in the medals or fans but I just wanted to help out when I can so sorry for leaving you! I swear if you follow the steps, im pretty sure youll get the right answer. let me refer to you an expert @SolomonZelman who can probably explain everything 10x better

Answer 59

ok what do i do next? can you just write out the steps next quickly? im likea visual learner hahah

Answer 60

plug in the x you found into the velocity function and bam, your answer. remember to round to 3 decimal places

Answer 61

oh and you said i was wrong???

Answer 62

I'm sorry. I don't know what I said was wrong for you. I probably misunderstood what you wrote.

Answer 63

16x^2-500/40=x

Answer 64

oh, you should have an actual value for x.

Answer 65

not whatever that is

Answer 66

so what do i do since there is 2 x's?

Answer 67

what are these two x's?

Answer 68

0 = -16x^2 + 40x + 500 how do i solve for x? my last question!

Answer 69

you can use the quadratic equation or a graphing calculator. or factor if you can

Answer 70

-6100.96?

Answer 71

thats what my calc gave me, what did you get?

Answer 72

;_; um, as you said, there should be two values of x. and that one is very off. I didn't do it as I am doing my homework right now. I'm sure if you just recheck what your doing, you'll find out what went wrong! keep on going. i really have to go :(

Answer 73

ahhh okkk

Answer 74

thanks for al your help though(:

Answer 75

im confused cause you just said ill have two x's, but i plug one into my velocity..

Answer 76

@SithsAndGiggles can you please continue?! theres like nothing left, i just want to see if im headed the right direction(:

Answer 77

http://www.wolframalpha.com/input/?i=0+%3D+-16x%5E2+%2B+40x+%2B+500+solve+for+x

Answer 78

you have 2 x, but the first one is negative, and the time is NEVER negative, right? so, just get rid of the negative one

Answer 79

so x is just this (:

Answer 80

yes

Answer 81

so i plug this into -32x+40??

Answer 82

@freckles can you pleasee continue? he just left :/

Answer 83

@ganeshie8 THANK YOU SO MUC

Answer 84

@freckles

Answer 85

Yes! so far so good.. next plugin that value into velocity equation :
\[v(t) = -32t + 40\]

Answer 86

plugin t = t = 5/4 (1+sqrt(21)) and you're done

Answer 87

http://www.wolframalpha.com/input/?i=-32%285%2F4+%281%2Bsqrt%2821%29%29%29+%2B+40

Answer 88

did you get -183.303???

Answer 89

oh cool(: thank you!!

Answer 90

remove negative sign as the question is about speed, not velocity

Answer 91

183.303 feet/sec looks good

Answer 92

ohh so just 183.30 ?

Answer 93

cause its in hundreths place

Answer 94

three decimal places means "thousandth place"

Answer 95

sorry! read it wrong hahah