Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.2, Problem 43E

(a)

To determine

To find: The speed of the rock just before it hits the ground just before it hits the bottom 30 sec later when the acceleration due to the gravity is 1.6 m/sec2 .

(a)

Expert Solution

Answer to Problem 43E

The value of the speed is 48 m/sec .

Explanation of Solution

Calculation:

Consider the acceleration is,

a(t)=1.6 m/sec2

Consider the velocity is the anti-derivative of the acceleration that is,

v(t)=1.6t+C=1.6t

Then,

v(t)=1.6(30)=48 m/sec

(b)

To determine

To find: The distance below the point of the release is the bottom of the crevasse.

(b)

Expert Solution

Answer to Problem 43E

The distance is of 720 m .

Explanation of Solution

Calculation:

Consider the expression for the distance is,

s(t)=1.6(12t2)+C=0.8t2

Then, after 30 sec is,

s(t)=0.8(30)2=720 m

(c)

To determine

To find: The time at which the rock will hit the bottom and the speed at which the rock will go.

(c)

Expert Solution

Answer to Problem 43E

The required time is 48.16 m/s .

Explanation of Solution

Given:

The rock instead of being released from the rest the rock is thrown into the crevasse from the same point with the downward velocity of 4 m/sec .

Calculation:

Consider the velocity is the anti-derivative of the acceleration that is,

v(t)=1.6t+C

Then,

v(0)=1.6(0)+CC=4

Then, the equation is,

v(t)=1.6t+4

Then, the distance travelled is,

s(t)=0.8t2+t+C=0.8t2+4t

Then,

720=0.8t2+4tt=−5±51452t=27.60,−32.60

Then, the velocity is,

v(27.60)=1.6(27.60)+4=48.16 m/s

Chapter 5.2, Problem 42E

Chapter 5.2, Problem 44E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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