BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 63E
To determine

To evaluate: The maximum height attained by the ball.

Expert Solution

Answer to Problem 63E

The maximum height attained by the ball is 25ft .

Explanation of Solution

Given:

A ball through directly upward with the velocity of 40ft/s , the function of height(in feet) after t second is given by y=40t16t2 .

Calculation:

The function of height (in feet) after t second is given by,

y=40t16t2=16t2+40t (1)

The standard form of function,

f(t)=at2+bt+c (2)

The maximum or minimum value of the function occurs at,

t=b2a (3)

If a>0 , then the minimum value is f(b2a) .

If a<0 , then the maximum value is f(b2a) .

From the equation (1) and (2),

a=16b=40

Substitute 16 for a and 40 for b in the equation (3),

t=402×(16)=54

The function has maximum value,

a=16<0 .

The maximum value of the function at t=54 ,

f(54)=40×(54)16×(54)2=(10×5)(1×25)=5025=25

The maximum value of the function y=40t16t2 is 25 .

Thus, the maximum height attained by the ball is 25ft .

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