Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 17

Each minute, a special game warden's machine gun fires 220 , 12.6-g rubber bullets with a muzzle velocity of \(975 \mathrm{~m} / \mathrm{s}\). How many bullets must be fired at an \(84.7-\mathrm{kg}\) animal charging toward the warden at \(3.87 \mathrm{~m} / \mathrm{s}\) in order to stop the animal in its tracks? (Assume that the bullets travel horizontally and drop to the ground after striking the target.)

Short Answer

Expert verified
To stop the animal in its tracks, approximately 27 bullets are required.

Step by step solution

01

Calculation of Animal's Momentum

Firstly, calculate the momentum of the charging animal. Momentum is the product of mass and velocity, so calculate it as \( Momentum = Mass_{animal} \times Velocity_{animal} = 84.7 kg \times 3.87 m/s = 327.869 kg \cdot m/s \)
02

Calculation of Bullet's Momentum

Next, calculate the momentum of a single bullet. Remember that the bullet's mass needs to be in kilograms, so convert the given mass from grams to kilograms. \(Mass_{bullet} = 12.6g = 12.6/1000 kg = 0.0126 kg \). Now calculate the bullet's momentum as \( Momentum_{bullet} = Mass_{bullet} \times Velocity_{bullet} = 0.0126 kg \times 975 m/s = 12.285 kg \cdot m/s \)
03

Number of Bullets Required

To stop the animal, the total momentum imparted by the bullets must equal the animal's momentum. Thus, calculate the number of bullets required as \(Number_{bullets} = Momentum_{animal} / Momentum_{bullet} = 327.869 kg \cdot m/s / 12.285 kg \cdot m/s \). Round this value up to the nearest whole number since we can't have fractional bullets.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

A rocket at rest in space, where there is virtually no gravity, has a mass of \(2.55 \times 10^{5} \mathrm{~kg}\), of which \(1.81 \times 10^{5} \mathrm{~kg}\) is fuel. The engine consumes fuel at the rate of \(480 \mathrm{~kg} / \mathrm{s}\), and the exhaust speed is \(3.27 \mathrm{~km} / \mathrm{s}\). The engine is fired for \(250 \mathrm{~s}\). (a) Find the thrust of the rocket engine. \((b)\) What is the mass of the rocket after the engine burn? \((c)\) What is the final speed attained?

A shell is fired from a gun with a muzzle velocity of \(466 \mathrm{~m} / \mathrm{s}\), at an angle of \(57.4^{\circ}\) with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming level terrain?

A Plymouth with a mass of \(2210 \mathrm{~kg}\) is moving along a straight stretch of road at \(105 \mathrm{~km} / \mathrm{h}\). It is followed by a Ford with mass \(2080 \mathrm{~kg}\) moving at \(43.5 \mathrm{~km} / \mathrm{h}\). How fast is the center of mass of the two cars moving?

Twelve \(100.0\) -kg containers of rocket parts in empty space are loosely tethered by ropes tied together at a common point. The center of mass of the twelve containers is originally at rest. A 50 -kg lump of "space-goo" moving at \(80 \mathrm{~m} / \mathrm{s}\) collides with one of the containers and sticks to it. (a) Assuming that none of the tethers break, find the speed of the center of mass of the twelve containers after the collision with the space goo. (b) Assuming instead that the tether of the struck container does break, find the speed of the center of mass of the twelve containers after the collision.

A rocket of total mass \(1.11 \times 10^{5} \mathrm{~kg}\), of which \(8.70 \times 10^{4} \mathrm{~kg}\) is fuel, is to be launched vertically. The fuel will be burned at the constant rate of \(820 \mathrm{~kg} / \mathrm{s}\). Relative to the rocket, what is the minimum exhaust speed that allows liftoff at launch?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Classical Mechanics

Read Explanation

Fluids

Read Explanation

Fundamentals of Physics

Read Explanation

Waves Physics

Read Explanation

Electricity and Magnetism

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.

Sign-up for free