   Chapter 13.4, Problem 27E

Chapter
Section
Textbook Problem

# A rifle is fired with angle of elevation 36°. What is the muzzle speed if the maximum height of the bullet is 1600 ft?

To determine

To find: The muzzle speed if the maximum height of the bullet is 1600 ft.

Explanation

Given:

α=36° and y=1600ft .

Formula:

Write the expression for position vector of the projectile.

r(t)=(v0cosα)ti+[(v0sinα)t12gt2]j (1)

Here,

v0 is the initial speed,

g is the gravity, which is 32fts2 , and

α is the angle of elevation.

The parametric equations of the trajectory are,

x=(v0cosα)t

y=(v0sinα)t12gt2 (2)

Write the expression for velocity.

v(t)=r(t)

v(t)=ddt[r(t)]

Take differentiation with respect to t on both sides of equation (1).

ddt[r(t)]=ddt{(v0cosα)ti+[(v0sinα)t12gt2]j}=ddt[(v0cosα)ti]+ddt[(v0sinα)t12gt2]j=(v0cosα)i+[(v0sinα)12g(2t)]j=(v0cosα)i+[(v0sinα)gt]j

Substitute v(t) for ddt[r(t)] ,

v(t)=(v0cosα)i+[(v0sinα)gt]j (3)

The shell reaches the maximum height when the vertical component of velocity is zero

### 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

#### Convert the expressions in Exercises 6584 to power form. xx

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 23-36, find the domain of the function. 26. g(x)=2x+1x1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### The center of 4x2 + 8x − 3y2 + 12y + 4 = 0 is (1, −2) (−1, 2) (2, −1) (−2, 1)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: These lines are skew:

Study Guide for Stewart's Multivariable Calculus, 8th 