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Sedaia [141]
3 years ago
10

A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time

Mathematics
2 answers:
Reika [66]3 years ago
4 0
<h2>Maximum height reached is 6.5 ft</h2>

Step-by-step explanation:

Equation is given by p(t) = 3gt² + v₀t + P₀

Given that

                g = -32 ft/s²

                v₀ = 24 ft/s

                P₀ = 5 ft

Substituting

              p(t) = 3 x -32 x t² + 24 x t + 5

              p(t) = -96 t² + 24 t + 5

We need to find maximum of this equation, at maximum we have derivative is zero.

              p'(t) = -96 x 2t + 24 = 0

             192 t = 24

                    t = 0.125 s

Substituting in p(t) equation

              p(0.125) = -96 x 0.125² + 24 x 0.125 + 5

              p(0.125) = 6.5 ft

Maximum height reached is 6.5 ft

FinnZ [79.3K]3 years ago
3 0

If the ball was thrown straight up at 24 ft/sec when it was 5 ft above the ground, the ball reached a maximum height of 7.25 m

\texttt{ }

<h3>Further explanation</h3>

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

<h2>D = b² - 4 a c</h2>

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

\texttt{ }

An axis of symmetry of quadratic equation y = ax² + bx + c is :

\large {\boxed {x = \frac{-b}{2a} } }

Let us now tackle the problem!

\texttt{ }

<u>Given:</u>

p(t) = 3gt^2 + v_ot + p_o

p(t) = 3(-32)t^2 + 24t + 5

p(t) = -64t^2 + 24t + 5

<u>Asked:</u>

p_{max} = ?

<u>Solution:</u>

<em>At the maximum height , velocity is 0 m/s:</em>

v = \frac{dp(t)}{dt}

v = \frac{d}{dt} ( -64t^2 + 24t + 5 )

v = (-64)(2)t^{2-1} + 24

v = -128t + 24

0 = -128t + 24

128t = 24

t = 24 \div 128

t = 3 \div 16

t = 0.1875 \texttt{ s}

\texttt{ }

p(t) = -64t^2 + 24t + 5

p(0.1875) = -64(0.1875)^2 + 24(0.1875) + 5

p(0.1875) = 7.25 \texttt{ m}

\texttt{ }

<h3>Learn more</h3>
  • Solving Quadratic Equations by Factoring : brainly.com/question/12182022
  • Determine the Discriminant : brainly.com/question/4600943
  • Formula of Quadratic Equations : brainly.com/question/3776858

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

\texttt{ }

Keywords: Quadratic , Equation , Discriminant , Real , Number

#LearnWithBrainly

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