Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A rifle is used to shoot twice at a target, using identical cartridges. The first time, the rifle is aimed parallel to the ground and directly at the center of the bull’s-eye. The bullet strikes the target at a distance of H$_A$ below the center, however. The second time, the rifle is similarly aimed, but from twice the distance from the target. This time the bullet strikes the target at a distance of $H_{{B}}$ below the center. Find the ratio $H_{{B}} / H_{{A}}$

$\frac{H_{B}}{H_{A}}=4$

Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Washington

Simon Fraser University

University of Sheffield

Lectures

04:16

In mathematics, a proof is…

04:48

In mathematics, algebra is…

05:53

Certain rifles can fire a …

01:37

A rifle is aimed horizonta…

00:36

A high-powered rifle fires…

03:44

(II) A hunter aims directl…

07:23

A hunter aims directly at …

02:40

0:00

Bull’s-eye Bob at a huntin…

04:15

A rifle that shoots bullet…

02:55

A horizontal rifle is fire…

04:30

The three targets from a r…

07:36

ssm From the top of a tall…

07:12

The speed of a bullet as i…

04:46

01:50

A .22 caliber gun fires a …

01:13

A bullet is fired horizont…

A projectile is being laun…

09:39

01:56

Use the following fact: Wh…

The velocity of a bullet f…

06:21

Range and height versus sp…

So the question states that two rifles air shot at a target, and the first rifle is shot parallel to the um to the ground, and the bullet hits a distance H a below the target center. And the second, uh, rifle is shot twice the distance that A J was shot from. And the bullet Glanz h sub be below the below the target. And we're trying to find the ratio between HCV and it's of a. So the first thing we need to do is use our kingdom attic equations to come up with this ratio. So we know that the change in displacement in the Y direction is equal to the changing this the initial velocity in the Y direction times time close 1/2 times the acceleration times time squared. And we know that because the bullet is shot in the horizontal direction parallel to the ground, there's gonna be no initial vertical velocity, so this term will cancel out. So we're just left with this, um and so we can tailor this to our problem because we know the displacement in the Y direction is h sabian. It's of any. So let's say, for bullet be. The displacement is it's a B, and it's equal to 1/2 times acceleration, which is going to be negative 9.8 times the time, which we don't know. We'll just call it T sabih squib. And same thing goes for H soap A where the acceleration is gonna be the exact same. But the time is going to be different. So now that we know this, we can simplify this by taking it. So be and dividing it by each sub a and we get the relationship that we wanted So it's gonna be time of bullet B squared, divided by the time of bullet A squared. So now that we know this relationship, we need to find something where we can substitute in for this time here. Um, And to do this, we can look at the range of the bullet. So we know the range equation states that the velocity in the horizontal direction it's safer be times the time for B is equal to the range for B and same thing goes for a times. The time for a is equal to the range for a and so we can divide by, uh, T on both sides and so we'll get velocity. Herbie is equal to three range for be divided by the time for B and this is the bossy for a is equal to the range for a But by the time pray and we know that both the bullets are shot at the same speed. So these two terms have to be equal to each other. So we considered equal. So we'll see that Exelby, where t should be is equal to X of a over tea soap A. And we also know that the uh range of Exelby is twice the range of X. A base knew the Exelby equals two times X obey. So we can plug this into here. And when we do this, we get to accept a over T B equals X up a over t a. We can simplify this more by multiplying by t b on both sides and we'll get and also dividing by exhibition. Besides, and we'll get TB over. T A is equal to two x of a over X A which is equal to two. So we know TB over ta is equal to two, which means T B squared over ta squared is equal before so which means TB squared over t A squared is he called the two squared, So this means that H B over H A is equal to four.

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, a proof is a sequence of statements given to explain how a c…

In mathematics, algebra is one of the broad parts of mathematics, together w…

Certain rifles can fire a bullet with a speed of 965 $\mathrm{m} / \mathrm{s…

A rifle is aimed horizontally at a target 30 $\mathrm{m}$ away. The bullet h…

A high-powered rifle fires a bullet with a muzzle speed of 1.00 km/s. The gu…

(II) A hunter aims directly at a target (on the same level) 75.0 $\mathrm{m}…

A hunter aims directly at a target (on the same level) 68.0 $\mathrm{m}$…

A rifle is aimed horizontally at a target 50 m away. The bullet hits the tar…

Bull’s-eye Bob at a hunting range fires his rifle at a target 200 meters dow…

A rifle that shoots bullets at 460 $\mathrm{m} / \mathrm{s}$ is to be aimed …

A horizontal rifle is fired at a bull’s-eye. The muzzle speed of the bullet …

The three targets from a rifle range shown below were produced by: (A) the i…

ssm From the top of a tall building, a gun is fired. The bullet leaves the g…

The speed of a bullet as it travels down the barrel of a rifle toward the op…

A .22 caliber gun fires a bullet at a speed of 1200 feet per second. If a .2…

A bullet is fired horizontally from a pistol, and another bullet is dropped …

A projectile is being launched from ground level with no air resistance. You…

A projectile is being launched from ground level with noair resistance. …

Use the following fact: When a projectile (such as a ball or a bullet) leave…

The velocity of a bullet from a rifle can be approximated by $v(t)=6400 t^{2…

Range and height versus speeda. Show that doubling a projectile's i…

02:23

In $1998,$ NASA launched Deep Space $1(\mathrm{DS}-1),$ a spacecraft that su…

05:39

Two particles are located on the $x$ axis. Particle 1 has a mass $m$ and is …

04:41

A person who walks for exercise produces the position-time graph given with …

05:12

The drawing shows a device that you can make with a piece of cardboard, whic…

03:37

A golfer rides in a golf cart an average speed of 3.10 $\mathrm{m} / \mathrm…

04:32

A space probe has two engines. Each generates the same amount of force when …

03:07

A 40.0-kg boy, riding a 2.50-kg skateboard at a velocity of +5.30 m/s across…

03:03

Bicyclists in the Tour de France reach speeds of 34.0 miles per hour (mi/h) …

07:44

ssm A $325-\mathrm{kg}$ boat is sailing $15.0^{\circ}$ north of east at a sp…