Question

help really stressed
A juggler is performing her act using several balls. She throws the balls up at an initial height of 4 feet, with a speed of 15 feet per second. If the juggler doesn't catch one of the balls, about how long does it take the ball to hit the floor?

Hint: Use H(t) = −16t2 + vt + s.

Answer 1

please help me

Answer 2

\[h(t) = -16t^2 + vt + S\]
We have an initial height of 4 feet
in the equation, this is s ..we are also given a speed of 15 feet/second

Answer 3

I think the quadratic function will work for this

Answer 4

after plugging in everything

Answer 5

in the equation, this is V and we are interested in the amount of time it iwll take for the ball to drop tot he ground

at this time, height will be zero
\[h(t)=−16t^2+vt+S \space = 0\]

Answer 6

so what we have here is a quadratic equation,
we can solve this using the quadratic formula like @Mehek14 said

Answer 7

\(\bf{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}\)

Answer 8

original formula is
\(\bf{f(x)=ax^2+bx+c}\)

Answer 9

for a, you have -16
for b, you have 15
and for c, you have 4
@jaredhm29 can you plug that into the quadratic formula?

Answer 10

@jaredhm29 are you there?

Answer 11

yes

Answer 12

Ive had a stuggle in this segment

Answer 13

@Mehek14

Answer 14

can you plug a, b , and c into the quadratic formula?

Answer 15

idk what u mean sry

Answer 16

\(\bf{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}\)

Answer 17

for a, you have -16
for b, you have 15
and for c, you have 4

Answer 18

\(\bf{x=\dfrac{-15±\sqrt{15^2-4*(-16)*4}}{2*(-16)}}\)

Answer 19

first thing
what is
\(15^2=?\)

Answer 20

@jaredhm29 ?

Answer 21

@Theloshua

Answer 22

please help me @Miracrown

Answer 23

@zzr0ck3r @Miracrown

Answer 24

@mathmate

Answer 25

As @Miracrown said,
\(\large h(t) = -16t^2 + vt + S\)
is a standard kinematics equation giving the height h above datum (ground) at time t (therefore h(t)) as a function of t.
v is the initial velocity (up = positive)=15 ft/s, and S= initial location (4 ft above datum= ground).
-16 is actually acceleration due to gravity (32.2 ft/s^2) divided by 2, negative because acceleration is downwards.
Substitute these values, you will get the same equation as @mehek14 showed you.
Solving for t and reject the negative root gives you the time required.