   Chapter 9.6, Problem 37E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Ballistics Ballistics experts are able to identify the weapon that fired a certain bullet by studying the markings on the bullet. Tests are conducted by firing into a bale of paper. If the distance s, in inches, that the bullet travels into the paper is given by s   =   27   −   ( 3   −   10 t ) 3 for 0 ≤ t ≤ 0.3 second, find the velocity of the bullet one-tenth of a second after it hits the paper.

To determine

To calculate: The velocity of the bullet if in one-tenth of a second after it hits the paper if the distance s, in inches, that the bullet travels into the paper is given by, s=27(310t)3 where 0t0.3.

Explanation

Given Information:

The bullet travels into the paper is given by, s=27(310t)3 where 0t0.3.

Formula used:

According to the power rule, if f(x)=xn,

Then, f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

According to the product rule, if f(x)=u(x)v(x), then

f(x)=u(x)v(x)+v(x)u(x)

According to the property of differentiation, if a function is of the form y=un, where u=g(x),

dydx=nun1dudx

Calculation:

Consider the provided function,

s=27(310t)3

Consider (310t) to be u,

s=27u3

Differentiate both sides with respect to t,

dsdt=ddt(27u3)=ddt(27)ddt(u3)

Simplify using the power rule and rule for co

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 