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

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