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 61E

To determine

To calculate: The time for which the ball is in the air.

Expert Solution & Answer

Answer to Problem 61E

The required time for which the ball is in the air is 5.66 seconds.

Explanation of Solution

Given information:

The initial height of the ball = 7 feet

The initial vertical velocity = 90 feet

The height of the ball when the other player catches it = 3 feet

Formula used:

Quadratic formula:

x=−b±b2−4ac2a

Calculation:

Consider the required time be t , the initial height be h0 , the initial vertical velocity be v0 and the height of the ball when the other player catches it be h .

So, h0=7 , v0=90 and h=3

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

h=−16t2+v0t+h0

Substitute 90 for v0 , 7 for h0 and 3 for h in the above equation and simplify for t .

3=−16t2+90t+716t2−90t−7+3=016t22−90t2−42=028t2−45t−2=0

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

Substitute −45 for b , 8 for a and −2 for c in the above formula.

t=−(−45)±(−45)2−4(8)(−2)2(8)=45±45.7116

Solve for t further.

t=45+45.7116=5.66

And, t=45−45.7116=−0.04

The value of t cannot be negative.

Hence, the required time for which the ball is in the air is 5.66 seconds.

Chapter 3.4, Problem 60E

Chapter 3.4, Problem 62E

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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