BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Question

Chapter 3.4, Problem 63E

To determine

To calculate: The time for which the opposing team has to return the ball before it bounces the court.

Expert Solution & Answer

Answer to Problem 63E

The required time for which the opposing team has to return the ball before it bounces the court is 3.61 seconds.

Explanation of Solution

Given information:

The initial height of the ball = 10 feet

The initial vertical velocity = 55 feet per second

Formula used:

Quadratic formula:

$x=−b±b2−4ac2a$

Calculation:

Consider the required time be t , the initial height be $h0$ and the initial vertical velocity be $v0$ .

So, $h0=10$ , $v0=55$ and $h=0$

The model of the throwing of the ball can be written as:

$h=−16t2+v0t+h0$

Substitute 55 for $v0$ , 10 for $h0$ and 0 for h in the above equation and simplify for t .

$0=−16t2+55t+1016t2−55t−10=0$

To solve the above equation for t , use the quadratic formula $x=−b±b2−4ac2a$ .

Substitute −55 for b , 16 for a and −10 for c in the above formula.

$t=−(−55)±(−55)2−4(16)(−10)2(16)=55±3025+64032=55±366532=55±60.5432$

Solve for t further.

$t=55+60.5432=115.5432=3.61$

And, $t=55−60.5432=−5.5432=−0.17$

The value of t cannot be negative.

Hence, the required time for which the opposing team has to return the ball before it bounces the court is 3.61 seconds.

Chapter 3.4, Problem 62E

Chapter 3.4, Problem 64E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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