Question

If Bob throws a water balloon out of his dorm room window, which is 39 feet off the ground, and the initial velocity is 96 ft/sec, how long until the water balloon hits the ground? Use h=vt-16t^2

Answer 1

in this case, h = 39 and v = 96. Plug those values in and solve for t

Answer 2

That wouldn't work though because I am trying to find the time at height 0 (when it hits the ground)

Answer 3

then maybe h = 0 will work

Answer 4

h=0 and still the velocity of 96

Answer 5

but the issue is that we don't account for the 39 ft

Answer 6

hmm

Answer 7

maybe the equation should be h(t) = vt-16t^2+h

Answer 8

The equation in the question is the one my teacher gave

Answer 9

So I don't think that I am allowed to use a different one

Answer 10

alright

Answer 11

then use h = 0 and v = 96 and see if it works

Answer 12

\[0=96t-16t^2\]
\[16t^2-96t=0\]
\[t^2-6t=0\]
\[(t+2)(t-3)=0\]
\[t=-2 t=3\]

Answer 13

there should be a space between t=-2 and t=3

Answer 14

t^2-6t=0 does NOT turn into (t+2)(t-3)=0

Answer 15

t^2-6t=0 turns into t(t-6) = 0

Answer 16

Yeah sorry

Answer 17

so t=0 and t=6

Answer 18

yes

Answer 19

although, i'm not sure about the equation you're given, so idk 100%

Answer 20

Except my teacher had said that it would not factor evenly and we'd have to use the quadratic formula

Answer 21

So I am quite stuck.

Answer 22

so maybe there's a typo somewhere?

Answer 23

Our notes packet says \[h=vt-4.9t\] for meters and \[h=vt-16t^2\] for feet

Answer 24

I have a feeling it's something like

h=vt-16t^2

39=96t-16t^2

which would lead you to have to use the quadratic formula, but again not 100% sure

Answer 25

That should be \[h=vt-4.9t^2\]

Answer 26

but I'm more used to h(t) = -16t^2 + vt + h

Answer 27

so

h(t) = -16t^2 + vt + h

h(t) = -16t^2 + 96t + 39

then you plug in h(t) = 0 and solve for t

Answer 28

I am looking in my notes and the example equation is
"A ball is thrown directly upward from ground level with an initial velocity of 80 ft/sec. When will the ball return to the ground? How high will the ball go?"
h=80t-16t^2
0=16t(t-5)
t=0, t=5

h=80(2.5)-16(2.5)^2
h=200-100
100 feet

Answer 29

notice how this one is thrown from the ground level (height = 0)

Answer 30

but for this one says "Bob throws a water balloon out of his dorm room window, which is 39 feet off the ground"

the starting height is 39 ft

Answer 31

So you do think that I should use 39=96t-16t^2

Answer 32

more like 0 = -16t^2 + 96t + 39

Answer 33

0 = -16t^2 + vt only applies when you start on the ground

Answer 34

that +39 bumps everything up 39 so you start up 39 ft

Answer 35

So instead of equaling 39 (which would end up subtracting it), we add 39?

Answer 36

yeah solve 0 = -16t^2 + 96t + 39 for t

Answer 37

and the quadratic formula will have to be used

Answer 38

Okay, thank you so much!

Answer 39

np