Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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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 A Bridge To Success Algebra 2: 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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