Question

2. If a stone is tossed from the top of a 250 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 250, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.

Answer 1

Calc course?

Answer 2

The type of course this is affects the method for finding the answer.

Answer 3

what you mean

Answer 4

-9.8t^2-10t+250 = 0

Answer 5

do you know what to do from there?

Answer 6

Ah, nevermind. Didn't read the question carefully. No calculus necessary.

Answer 7

zzr0cker has it right. When it hits the ground, its height is 0. So set the height equal to 0 and solve for t.

Answer 8

make h=0 because h at ground is 0 and calculate time
neglect -ve time from the 2 roots

Answer 9

what

Answer 10

4.57 sec

Answer 11

but how

Answer 12

because i want to learn it

Answer 13

Okay, so they give us an equation for height based on time, right?
Do you agree that the height when it hits the ground is 0?

Answer 14

yes

Answer 15

Cool, so let's set our equation for height to 0 and figure out what value of t makes it true. Like this:
-9.8t^2 - 10t +250 = 0
solve for t.

And do you remember how to solve an equation of the form Ax^2 + Bx + C = 0?

Answer 16

no i drop out of school just recenlty enroll back in sorry

Answer 17

there are many ways, what are you guys doing in class? Does A C method sound familiar? or completing the square? or (-b +- sqrt(b^2-4ac))/2a

Answer 18

It's okay. There's this cool formula that looks complicated and fancy, but is actually pretty easy to use. It's called the quadratic formula and it works whenever we have an equation like Ax^2 + Bx + C = 0.
Figure out what A, B, and C are and plug them in to solve for x:
\[\frac{-B \pm \sqrt{B^2-4AC}}{2A}\]

Answer 19

ok

Answer 20

What are A, B, and C?

Answer 21

you could also graph it and see where it crosses the x-axes it all depends on what your teacher wants

Answer 22

wait am still lost

Answer 23

Here is a video, if you have time
http://www.khanacademy.org/math/algebra/quadtratics/v/introduction-to-the-quadratic-equation

Answer 24

Let me show you a simple example of myself using the formula.
Suppose I'm trying to solve the equation
\[2x^2 +2x -12 = 0\]
First, I notice that the equation looks like
\[Ax^2 + Bx + C =0\]
With A = 2, B=2, and C =-12
So, that means to solve, I can plug those into:
\[\frac{-B \pm \sqrt{B^2-4AC}}{2A}\]
So, I get:
\[\frac{-2 \pm \sqrt{2^2 -4*2*(-12)}}{2*2}\]

Answer 25

Doing a little bit of math on that gives me:
\[\frac{-2 \pm \sqrt{4-(-96)}}{4}\]
which gives
\[\frac{-2 \pm \sqrt{100}}{4}\]
so I get
\[\frac{-2 \pm 10}{4}\]

Answer 26

I get two answers from that. One comes from using a plus sign
\[\frac{-2+10}{4} = \frac{8}{4} = 2\]
The other comes from using a minus sign
\[\frac{-2-10}{4} = \frac{-12}{4} = -3\]

Answer 27

So that tells me, with just a little bit of work, that the solutions to my original equation are x=2, and x=-3.
The cool thing about the equation is that it ALWAYS works! =D

Answer 28

So, for your problem
-9.8t^2 -10t +250 = 0
it's the same exact process, but A, B, and C are different numbers, and your answers won't be such pretty integers like I got. They'll be decimals.

Answer 29

Oh, and you'll get one positive answer and one negative answer. The negative answer says that it hits the ground BEFORE he dropped it, which doesn't make any sense. So we ignore that one. The positive answer is correct though.

Give it a try, and ask me any questions you have.

Answer 30

Are you allowed to use calculus? It would ba a lot easier

Answer 31

yes

Answer 32

Actually, Naomi, since it doesn't ask for the maximum height of the projectile, but just when it lands, it really doesn't require any calculus.

Answer 33

o

Answer 34

I'm merely suggesting another way he could do it.

Answer 35

i dont understand

Answer 36

Do you know how to get derivatives? If not then follow Smoothmath's method without calculus

Answer 37

I dont see how setting a function equal to zero can get any easier, how would you do this in a "easier" way with calc?

Answer 38

I'm with zz. I don't think derivatives actually do anything for you in this problem.