Chapter 5.1, Problem 59E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Finding a Derivative In Exercises 43-66. find the derivative of the function. y = ln x + 1 x − 1

(a)

To determine

To calculate: The time in second after its release will the bag strikes the ground, if the rising velocity of ball is 16 feet per second.

Explanation

Given:

A balloon is rising vertically with a velocity of 16Â feetÂ perÂ second, release a sandbag at the instant it is 64 feet above the ground.

Formula used:

Integration, âˆ«xndx=xn+1n+1+C.

Calculation:

Let t=0 represent the initial time and the position of the object is y at any instant. Release a sandbag at the instant it is 64 feet above the ground.

y(0)=64

The initial velocity of sandbag and balloon are equal. So, the initial velocity of sand bag is,

yâ€²(0)=16

Since, the acceleration due to gravity g=âˆ’32Â feetÂ perÂ secondÂ perÂ second. So, the equation is written as,

yâ€³=âˆ’32

Integrate the above equation with respect to t,

yâ€²=âˆ«âˆ’32dt=âˆ’32t+C1

Let the initial velocity of the sand bag is yâ€²(0)=16. Now, find the value of C1,

yâ€²(0)=âˆ’32(0)+C116=C1

Now, the equation yâ€² is written as,

yâ€²=âˆ’32t+16 â€¦â€¦ (1)

Again, integrate the above equation,

y

(b)

To determine

To calculate: The velocity of the bag at the time when sandbag hit the ground, if the rising velocity of ball is 16 feet per second.

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