Question

PLEASE help me ? A bird sees a worm on the ground 50 m. below. The bird dives for the worm at a speed of 6 m/sec. The function h(t)= - 4.9t^2+6t+50, where h(t) is the height of the bird at time t. How long does the worm have before he is eaten?

Answer 1

Set h(t) = 0 and solve for t.

Answer 2

how would i write that with this problem?

Answer 3

note that h(0) = 50 meters. That is, at the start of the fall, the bird is 50 meters.

Answer 4

h(t)=0=-4.9t^2+6t+50

Answer 5

-4.9t^2+6t=-50

Answer 6

-4.9t^2+6t + (6/(2*4.9)^2=-50+(6/(2*-4.9)^2

Answer 7

-18.01 fo the first part of the problem

Answer 8

is that right

Answer 9

Bottom, line. You'll have a quadratic, one positive, one negative. Take the positive:
Solve for t over the real numbers:
0 = -4.9 t^2+6 t+50
Reverse the equality in 0 = -4.9 t^2+6 t+50 in order to isolate t to the left hand side.
0 = -4.9 t^2+6 t+50 is equivalent to -4.9 t^2+6 t+50 = 0:
-4.9 t^2+6 t+50 = 0
Write the quadratic equation in standard form.
Divide both sides by -4.9:
t^2-1.22449 t-10.2041 = 0.
Solve the quadratic equation by completing the square.
Add 10.2041 to both sides:
t^2-1.22449 t = 10.2041
Take one half of the coefficient of t and square it, then add it to both sides.
Add 0.374844 to both sides:
t^2-1.22449 t+0.374844 = 10.5789
Factor the left hand side.
Write the left hand side as a square:
(t-0.612245)^2 = 10.5789
Eliminate the exponent on the left hand side.
Take the square root of both sides:
t-0.612245 = 3.25253 or t-0.612245 = -3.25253
Look at the first equation: Solve for t.
Add 0.612245 to both sides:
t = 3.86477 or t-0.612245 = -3.25253
Look at the second equation: Solve for t.
Add 0.612245 to both sides:
Answer: |
| t = 3.86477 or t = -2.64028

Answer 10

wow I had to do all that ????????????? and which one is the answer how can it be 2 ?

Answer 11

Answer: |
| t = 3.86477 or t = -2.64028

Answer 12

Take the positive.

Answer 13

Note that -4.9t^2+6t+50 at t = 3.86477 is zero. That is, the bird is on the ground and h(3.86477)=0.

Answer 14

so it can be 0

Answer 15

This shows it.

Answer 16

why don't you use the quadratic formula....

Answer 17

what is it

Answer 18

Here's a plot of the function for t=0 to t=4:

Answer 19

Note that at the beginning of time it is 50 meters up and at 3.9 seconds, it hit the ground (i.e. h(t) = 0)

Answer 20

I'll try 3.9...

Answer 21

If you learn the quadratic formulat as @paigeRG indicates, the solution is so much easier to solve.

Answer 22

idk if i should round it to 4.

Answer 23

Then the bird will go slightly past the ground (using 4).

Answer 24

That would probably hurt the bird.

Answer 25

lol true..

Answer 26

http://en.wikipedia.org/wiki/Quadratic_formula#Quadratic_formula

Answer 27

http://www.purplemath.com/modules/quadform.htm <-------- heres a website that explains the quadratic formula, just so you know for future reference.... if you don't want to use it now

Answer 28

Dude... @ybarrap you put your website before mine, not cool

Answer 29

ok how would i plug my numbers in for the equation ? whats a,b,c???

Answer 30

If it's any consolation, I think your source is a lot friendlier. @xoxox123, use @paigeRG 's link first.

Answer 31

I'll let @paigeRG take over from here :)

Answer 32

Well ill be here if you need anything @xoxox123

Answer 33

ok good cause i need your help. can u help me plug the numbers from my equation to the formula

Answer 34

@paigeRG

Answer 35

yes, so in the equation, there are three letters a b and c... a is the first term of the equation b is the second and c is the third term so A=-4.9 B=6 and C=50

Answer 36

okay i understand that..

Answer 37

\[-b \pm \sqrt{b^2-4(a)(c)}\] and so that would be over
\[2(a)\]

Answer 38

now you would plug in the terms...
and since there is a negative times a negative it would turn possative -4(-4.9)(50) -----> so it would be 36+980

Answer 39

to get what ..?

Answer 40

1016?

Answer 41

are you there ??

Answer 42

whats that sign next to -b ?

Answer 43

sorry I had to eat dinner

Answer 44

1016 is correct so now what you would do is find the two answers, that's what the sign nest to the -6 is. it stands for plus of minus.

Answer 45

itd okay and the answer is going to be 2 ?

Answer 46

\[-6\pm \sqrt{1016 }\] over 2(-4.9)=-9.8

Answer 47

That plus of mius sign i never seen it before.... how do you put it in the calc

Answer 48

so now what you would do is do \[-6+\sqrt{1016} \div -9.8\] thus getting your first x intercept, and for your second intercept you would do \[-6-\sqrt{1016}\div -9.8\]

Answer 49

It say error when i put it in the calc ??

Answer 50

so your two answers are -2.6 and 3.9 (both rounded to nearest tenth)

Answer 51

wait nvm i got the first one i got -9.25252601

Answer 52

you cant really put it into a calculator its just one of those formulas you have to memorize... our teacher made us memorize it with a song...

Answer 53

all you do is plug the terms into the correct places and basically simplify the equation down to where you can figure the points, if you haven't learned it yet you will soon so no worries

Answer 54

well how did you solve -6+√1016/-9.8

Answer 55

well that part you can solve with a calculator

Answer 56

thats what i did and got that longg decimal

Answer 57

that's fine I got long decimals too, but I rounded them to the nearest tenth... I told you the answers you should have gotten did you see them?

Answer 58

yeah i saw them i still have 3 more problems then im a submit my quiz. and see if its right

Answer 59

I still have 2 more problems dealing with the same thing you just did //:

Answer 60

oh goodness

Answer 61

i knoww >.< can u please help me ??

Answer 62

it would be really helpfull :(

Answer 63

I can try but I have math stuff to work on too so ill see what I can do

Answer 64

OK thanks so much here it is.... A rocket is fired straight up from a 60 ft. platform with an initial velocity of 96 ft/sec. The height of the rocket, h(t), is found using the function h(t) = - 16t^2 + 96t + 60 where t is the time in seconds.
Find the number of seconds required to reach the maximum height.

Answer 65

Maximum height... I always hated finding the height of stuff... Ill see what I can do...

Answer 66

i hate it too but okay ! thanks

Answer 67

okay I found the x intercepts im just trying to figure out the height

Answer 68

if you dont know that one can u help with this one ???
A ball is dropped from the top of a 550 ft. building. The function h(t ) = - 16t^2 + 50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds).
How long does it take the ball to reach the ground? Round your answer to the nearest hundredth of a second.

Answer 69

do you have multiple choices

Answer 70

no sadly its written response

Answer 71

for the rocket one Im positive its 3

Answer 72

wait!

Answer 73

okay I will try it

Answer 74

noooo

Answer 75

what ??

Answer 76

im triple checking, just wait

Answer 77

yup its 3

Answer 78

okay time for the last one

Answer 79

okay I hope its right :)

Answer 80

okay question, is the equation for the last question correct? is it supposed to be -16t^2+50 or is it supposed to be -16t^2+550.... is it plus 50 or plus 550

Answer 81

its 50

Answer 82

your positive? because it says its dropped from a 550 ft building... unlesing is 50 ft tall and not 550

Answer 83

oh wait i thought your talking about the equation was 50 ? but yess the ball dropped from a 500 ft building.. sorry misread

Answer 84

500 ft... okay

Answer 85

Are you possssssiiitivvve the equation has 50 at the end...

Answer 86

NO! its 550!! omg im going to rewrite this for you.

Answer 87

well do you have the link> just copy and paste it so I can see for myself what it says

Answer 88

I cant because you would need the password for my class. I'll copy it exactly the way it is. A ball is dropped from the top of a 550 ft. building. The function h(t)= -16t^2+50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds). How long does it take the ball to reach the ground? Round your answer to the nearest hundredth of a second.

Answer 89

1.77

Answer 90

is it rounded.

Answer 91

Yes its rounded....I still think the equation is wrong but what ever... hope you get it right

Answer 92

I just submited it

Answer 93

And did I help you in anyway shape or form

Answer 94

3 is right , but 1.77 is not when i got it wrong it said to Graph the function. Where on the graph is the ground represented?

Answer 95

x axis

Answer 96

I graphed it on a graphing calculator and checked it a dozen times, but it still sounded wrong... the equation sounded wrong I mean

Answer 97

no the problem is right i made sure i wrote it right.. and i got the bird one wrong!!!