Q. 496 A ball is thrown upward from the... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 496 (page 986)

A ball is thrown upward from the ground with an initial velocity of $112$ ft/sec. Use the quadratic equation $h = = 16 t^{2} + 112 t$ to find how long it will take the ball to reach maximum height, and then find the maximum height.

Short Answer

Expert verified

The maximum height is $196$ feet and it is reached after $\frac{7}{2}$ seconds.

Step by step solution

Step 1. Given information.

We have a quadratic equation $h (t) = - 16 t^{2} + 112 t$ and a ball is thrown upward from the ground with an initial velocity of $112$ ft/sec.

Find the maximum height by finding vertex.

We have:

$h (t) = - 16 t^{2} + 112 t$

$The 鈥� vertex 鈥� of 鈥� an 鈥� up - down 鈥� facing 鈥� parabola 鈥� of 鈥� the 鈥� form 鈥� y = a x^{2} + b x + c 鈥� is 鈥� x_{v} = - \frac{b}{2 a}$

$The 鈥� parabola 鈥� params 鈥� are : a = - 16, 鈥� b = 112, 鈥� c = 0 x_{v} = - \frac{b}{2 a} t_{v} = - \frac{112}{2 (- 16)} t_{v} = \frac{7}{2}$

Plug $t_{v} = \frac{7}{2}$ in the original equation to find $y_{v}$ :

$y_{v} = 196 Therefore 鈥� the 鈥� parabola 鈥� vertex 鈥� is (\frac{7}{2}, 鈥� 196) If 鈥� a < 0, 鈥� then 鈥� the 鈥� vertex 鈥� is 鈥� a 鈥� maximum 鈥� value If 鈥� a > 0, 鈥� then 鈥� the 鈥� vertex 鈥� is 鈥� a 鈥� minimum 鈥� value a = - 16 Maximum (\frac{7}{2}, 鈥� 196)$

Therefore, the maximum height is $196$ feet and it is reached after $\frac{7}{2}$ seconds.

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91影视

A ball is thrown upward from the ground with an initial velocity of $112$ ft/sec. Use the quadratic equation $h = = 16 t^{2} + 112 t$ to find how long it will take the ball to reach maximum height, and then find the maximum height.

Short Answer

Step by step solution

Step 1. Given information.

Find the maximum height by finding vertex.

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

A ball is thrown upward from the ground with an initial velocity of 112ft/sec. Use the quadratic equation h==16t2+112tto find how long it will take the ball to reach maximum height, and then find the maximum height.

Short Answer

Step by step solution

Step 1. Given information.

Find the maximum height by finding vertex.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Geometry

Applied Mathematics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

A ball is thrown upward from the ground with an initial velocity of $112$ ft/sec. Use the quadratic equation $h = = 16 t^{2} + 112 t$ to find how long it will take the ball to reach maximum height, and then find the maximum height.