Question

using the equasion, s= -16t^2+Vo t +So to make a mathematical model for an object shot into the air at 48 ft. per second beginning at a height of 160 ft., use the model to find the height of the object after 3 ft.
s=-144+144+160=160
however if we started at 160 would we not add the 140 ft. the object would have traveled in 3 sec. to the 160? Idk I thought I knew how to do this one

Answer 1

it has gone up and come back down

Answer 2

Vo is initial velocity and So is initial height. Based on what you have in the problem, the model would be
s=-16t^2+48t+160

So s(3) = -16(3)^2 + 48(3) + 160 = -16(9) + 144 + 160 = -144 + 144 + 160 = 160

This confirms your answer. So this means that it has returned to it's initial height. Imagine you shot it off a cliff over a valley. The object, after 3 seconds, is atthe same height as the cliff and dropping into the valley.

Answer 3

maximum height achieved at vertex which is
\[-\frac{b}{2a}=\frac{48}{62}=1.5\]

Answer 4

maximum height achieved at vertex, which is at
\[-\frac{b}{2a}=\frac{48}{32}=1.5\]

Answer 5

what mtbender said. sorry i didn't see it.

Answer 6

this is not the formula I am supposed to use and I do not understand

Answer 7

not looking for max at vertex

looking for @3 seconds

Answer 8

@satellite - using the vertex is also good since parabolas have vertical symmetry. since the vertex is half the timne of the 3seconds, it will have returned to the starting height at that point.

Answer 9

what you wrote it totally correct.

Answer 10

@sunyday - look at my post. it uses your formula.

Answer 11

thank you

Answer 12

yeah i didn't mean to interrupt you. site is slow. i just wanted to point out that it when up for 1.5 seconds and then started coming back down, so at 3 seconds it is at original height

Answer 13

now it wants to know how long it will take to hiut the ground

Answer 14

"went up" is what i meant to say. what goes up...

Answer 15

To find when it hits the ground, set your model equal to 0 and solve for t.

User the quadratic formula since I doubt the numbers will be nice.

Answer 16

Correction, they are nice...divide through by -16.

Answer 17

It'll factor nicely and your answer will be only the positive root

Answer 18

is it 0=16t^2+3

Answer 19

No, your model is s(t)=-16t^2+48t+160

Set this equal to 0. -16t^2+48t+160 = 0

If you divide through be -6, you get
t^2-3t-10 = 0
which factors nicely. Factor this and set the two factors equal to 0...that will give you your two times the height would be 0

Once answer will be positive and one will be negative. The negative one makes no since because our model only works for positive values of t.

Answer 20

Sorry...divide through by -16 not -6

Answer 21

I do not know how to do this please help

Answer 22

\[-16t^2+48t+160=0\]
\[t^2-\frac{3}{2}t-10=0\]

Answer 23

that is a mistake

Answer 24

divide by -16 get
\[t^2-3t-10=0\] that is better

Answer 25

so you get
\[(t-5)(t+2)=0\]
\[t=5\] or
\[t=-2\] and the negative answer makes no sense because we are not going backwards in time

Answer 26

That factors into \[(t-5)(t+2)=0\]
And since if ab=0 then either a=0 or b=0, you know that either t-5=0 or t+2=0. Solve each of these for t and your answer is the positive one.

Answer 27

This time, I was slow, @satellite. :)

Answer 28

ok but i do not get the part where you divide by 16 just what and how I am lost there

Answer 29

What is divided by 16

Answer 30

your model tells you the height of the object at time t. you want that height to be 0, so you set your model equation equal to 0 and solve for time t.

So, the times the object is at a height of 0 is found by solving \[-16t^{2} + 48t + 160 = 0\]
To make the problem easier, I am going to divide both sides of the equation by -16. I am doing this becasue I know that 16, 48, and 160 are all divisible by 16. I am dividing by negative 16 to make the lead coefficient positive.

In general , *anytime* you can make the coefficients smaller, do it...it makes the problem easier.

So after dividing you have \[t^{2}-3t-10=0\]
which you then factor as we mentioned above.