anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
please help me
Miracrown
  • Miracrown
\[h(t) = -16t^2 + vt + S\] We have an initial height of 4 feet in the equation, this is s ..we are also given a speed of 15 feet/second
Mehek14
  • Mehek14
I think the quadratic function will work for this

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Mehek14
  • Mehek14
after plugging in everything
Miracrown
  • Miracrown
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 \[h(t)=−16t^2+vt+S \space = 0\]
Miracrown
  • Miracrown
so what we have here is a quadratic equation, we can solve this using the quadratic formula like @Mehek14 said
Mehek14
  • Mehek14
\(\bf{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}\)
Mehek14
  • Mehek14
original formula is \(\bf{f(x)=ax^2+bx+c}\)
Mehek14
  • Mehek14
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?
Mehek14
  • Mehek14
@jaredhm29 are you there?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ive had a stuggle in this segment
anonymous
  • anonymous
@Mehek14
Mehek14
  • Mehek14
can you plug a, b , and c into the quadratic formula?
anonymous
  • anonymous
idk what u mean sry
Mehek14
  • Mehek14
\(\bf{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}\)
Mehek14
  • Mehek14
for a, you have -16 for b, you have 15 and for c, you have 4
Mehek14
  • Mehek14
\(\bf{x=\dfrac{-15±\sqrt{15^2-4*(-16)*4}}{2*(-16)}}\)
Mehek14
  • Mehek14
first thing what is \(15^2=?\)
Mehek14
  • Mehek14
@jaredhm29 ?
anonymous
  • anonymous
@Theloshua
anonymous
  • anonymous
please help me @Miracrown
anonymous
  • anonymous
@zzr0ck3r @Miracrown
anonymous
  • anonymous
@mathmate
mathmate
  • mathmate
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.

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