Question

The height of an object thrown vertically upward from a height of 25 feet is given by h(t) = -16t^2 + 128t +25 where the height is measured in feet and time is measured in seconds. How long does it take for the object to hit the ground?

Answer 1

you have a curious mind...

Answer 2

Physics

Answer 3

@vikayefremova

Answer 4

@ParthKohli @lgbasallote @lalaly

Answer 5

my job is over

Answer 6

over to you guys

Answer 7

So, we know that the height must be 0(it's the ground right?)
Solve this quadratic equation.

\( \color{Black}{\Rightarrow -16t^2 + 128 + 25 = 0}\)

Do you know how to solve quadratic equations?

Answer 8

I forgot, we learned this so long ago. o;

Answer 9

Use the quadratic formula here.

\( \color{Black}{\Rightarrow t = \Large {-b \pm\sqrt{b^2 - 4ac} \over 2a} }\)

Answer 10

a = -16
b = 128
c = 25

Use a calculator to do this.

Answer 11

Am I supposed to be getting huge numbers

Answer 12

No...not at all

Answer 13

Show me what you did please?

Answer 14

Ok assume you throw a ball upwards, it will get to a maximum height and then it will come down again right?
Reply Using Drawing
This is how it's path would look like
Forming a parabola. So when the ball comes back down, and hits the ground the height of the ball will be zero since it's on the ground. So to find the time it takes to hit the ground, we find the time when the height is equal to zero. So you just put h as o and solve for t. Factoring out -16t and then you would have -16t(t-4) = 0 Equations of such form give you two answers, 16t=0 which is just t=0 and t-4=0 which is t=4
I hope that helps.

This is a similar question

Answer 15

But for yours, using the quadratic formula, you can solve for t,
Just remember a= coefficient of x^2 b= coefficient of x and c = constant

Answer 16

Okay, thanks. o; But like, maybe I'm setting up the quadratic formula wrong which I shouldn't be.

Answer 17

t= \[(-128+/- \sqrt{(128)^{2}-4(-16\times25}))/2\times-16\]
That's what you should have

Answer 18

\[-128 \pm \sqrt{17225}/-32\]

Answer 19

Couldn't that be simplified more? o:

Answer 20

And wouldn't that add that imaginary thing..? idk

Answer 21

\[4±\sqrt{281}/-4\] This is how it would be, ignore my previous one

Answer 22

She told us that the answer is 8.19 seconds, so how would we get from that to there?

Answer 23

But then remember, time can not be negative, so you're answer would be \[4-\sqrt{281}/-4\]
Notice that if you try to do \[4+\sqrt{281}/-4\] it gives you a negative answer?

Answer 24

Mhm. But I still don't know how to get 8.19 seconds. :c

Answer 25

ok \[\sqrt{281}\] using a calculator is around 16.7631 if you divide that by -4, you get
-4.1908.
So now all you need to do is 4-(-4.1908)= 4+4.1908=8.19

Answer 26

Ohohoh. Okay. C: Tysm.