/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 81 A projectile fired into the firs... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q. 81 (page 458)

A projectile fired into the first quadrant from

the origin of a coordinate system will pass through the point

(x, y) at time t according to the relationship cot胃=2x2y+gt2,

where 胃= the angle of elevation of the launcher and g =

the acceleration due to gravity = 32.2ft/sec2

. An artilleryman is firing at an enemy bunker located 2450 feet

up the side of a hill that is 6175 feet away. He fires a round,

and exactly 2.27 seconds later he scores a direct hit.

(a) What angle of elevation did he use?

(b) If the angle of elevation is also given by sec胃=v0tx

x , wherev0is the muzzle velocity of the weapon, find the muzzle

velocity of the artillery piece he used.

Short Answer

Expert verified

(a) The angle of elevation is 22.3鈭�.

(b) The muzzle velocity is2940.20ft/sec.

Step by step solution

01

Part (a) Step 1. Given Information

An artilleryman is firing at an enemy bunker located 2450 feet

up the side of a hill that is 6175 feet away. He fires a round,

and exactly 2.27 seconds later he scores a direct hit.


02

Part (a) Step 2. Calculation

hill=6175ftenemy=2450ftcot胃=2(6175)2(2450)+(32.2)(2.27)=123505065.92338=2.4379therefore,胃=cot-12.4379=22.3鈭�

03

Part (b) Step 1. Calculation

Substitutex,tand胃intheequationsec22.3=v0(2.27)6175=0.0003676v0sec22.30.0003676=0.0003659v00.0003676v0=sec22.30.0003676=1.08080.0003676=2940.23

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Establish each identity.

1-2cos2胃sin胃cos胃=tan胃-cot胃

Show that the difference quotient for f(x)=cosxis given by


role="math" localid="1646431168099" f(x+h)-f(x)h=cos(x+h)-cos(x)h=-sinx路sinhh-cosx路1-coshh

The distance dfrom the point (2,-3)to the point (5,1)is ______.

solve each equation on the interval

3sin胃+cos胃=1

If x=2tan胃, express cos2胃as a function ofx.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.