Question

A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
a. Substitute the values into the vertical motion formulah=-16t^2+Vot+Ho Let h = 0.
b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
a.0=-16t^2+101t+116;8s
b.0=-16t^2+116t+101;0.8s
c.0=-16t^2+101t+116;0.8s
d.0=-16t^2+116t+101;8s

Answer 1

$$
\color{blue}{\text{A rocket is launched from atop a 101-foot}}\\
\color{green}{\text{ cliff with an initial velocity of 116 ft/s}}\\
h=-16t^2+\color{green}{V_o}t+\color{blue}{h_o}
$$

Answer 2

so, which one do you think is the equation?

Answer 3

vot

Answer 4

hmm?

Answer 5

well, look at your choices

Answer 6

so b or d

Answer 7

in the equation
$$ \large {
\color{green}{V_o} = \text{initial velocity}\\
\color{blue}{h_o} = \text{initial height} }
$$

Answer 8

so, what's the initial velocity for the rocket?
from what height it initially started traveling?

Answer 9

116ft/s

Answer 10

and the initial height?

Answer 11

anyhow, you're right, is 101ft, so is either B or D

Answer 12

notice the squared term has a negative number in front of it, that is \(\bf -16t^2+116t+101\
that means the parabola is opening downwards, so it'd look like

Answer 13

\(\bf -16t^2+116t+101\) that is

Answer 14

so d would be the appropriate answer

Answer 15

well, we dunno, the rocket will take "t" minutes to hit the ground on the way back down
when that happens, that is when the parabola hits the x-axis, y = 0
so \(\bf y = -16t^2+116t+101 \implies 0 =-16t^2+116t+101\)

Answer 16

\(\bf \text{quadratic formula}\\
x= \cfrac{ - b \pm \sqrt { b^2 -4ac}}{2a}\)

Answer 17

now if we plug the values in for that, that'd be
a = -16
b = 116
c = 101
\(\bf t= \cfrac{ - 116 \pm \sqrt { 16^2 -4(-16)(101)}}{2(-16)}\)

Answer 18

meh, I have a typo bleh

Answer 19

\(\bf t= \cfrac{ - 16 \pm \sqrt { 16^2 -4(-16)(101)}}{2(-16)}\)

Answer 20

there will be 2 values for "t", one for + root, and one for the - root
one number will be negative, you can rule that one out

Answer 21

since it's time and a negative time will mean the rocket was launched today and fell on the ground yesterday, which of course won't make much logical sense hehe

Answer 22

or not yesterday but a few mins ago