If the child in the previous additional in-class example pulls with an extra 2.0 n in the horizontal direction, what will be the acceleration of the shoe?

Answers

Answer 1

The acceleration of the shoe will depend on the mass of the shoe and the net force acting on it. Additional information is needed to determine the mass of the shoe.

In the absence of information about the mass of the shoe, we cannot directly calculate its acceleration. Acceleration is determined by dividing the net force acting on an object by its mass, according to Newton's second law of motion (F = ma).

If we know the mass of the shoe, we can calculate the acceleration by dividing the net force (the sum of the applied force and any other forces acting on the shoe) by the mass of the shoe.

Without the specific mass of the shoe, we cannot provide a numerical value for the acceleration.

However, we can state that if the child pulls with an extra 2.0 N in the , horizontal directionthe acceleration of the shoe will increase compared to the previous example where the child pulled with only a certain force.

The exact value of the acceleration would depend on the mass of the shoe and other forces involved in the system.

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Related Questions

Once an answer is submitted, you will be unable to return to this part. A 150-kg crate D is suspended from a ring at Aby a length of rope. The crate is held in certain location by two blocks, B and C, which are attached to the ring at Aby rope segments wrapped around frictionless pulleys. You want to position the crate such that the angle that rope AC makes in a counterclockwise direction from the positive x-axis is 30° as shown. The mass of block B is 135 kg. The mass of block C is adjustable. You decide to calculate what the mass of block C needs to be in order to keep crate D in the desired position. You also want to calculate , which represents the angle that rope AB makes in a clockwise direction from the negative x-axis when crate D is in the desired position. X 00:36:18 180° Choose which value represents the mass of block C that would keep crate D In equilibrium. Choose which value represents the mass of block C that would keep crate D In equilibrium. Multiple Choice 280 kg 20 kg 784.8 kg 196.2 kg 111.74 kg

Answers

The value that represents the mass of block C that would keep crate D in equilibrium is 196.2 kg (Option D).

To determine of value that represents the mass of block C that would keep crate D in equilibrium, ee can begin by determining the tension in the ropes. Since the crate is held in a certain location by two blocks, the tension in the ropes should be equal. We can use this fact to calculate the tension in the ropes by assuming that they have the same magnitude.

In this case, let T be the tension in each rope segment. The forces acting on the system can be represented in the following free-body diagram:

For the x-direction: T sin 30° = T sin 60° + µg = 0

where µ is the coefficient of friction and g is the acceleration due to gravity. Since the pulleys are frictionless, µ = 0. Therefore, we can simplify the equation as follows:

T sin 30° = T sin 60°

Dividing both sides by T:

sin 30° = sin 60°/2

This gives us: T = (2/√3) mg where m is the total mass of the system and g is the acceleration due to gravity.

Substituting the given values, we obtain:

T = (2/√3) × 150 × 9.81 ≈ 1962 N

Next, we can use the law of the lever to calculate the mass of block C required to keep the crate in equilibrium. According to this law, the sum of the moments acting on the system must be zero. We can choose the point where the ring is attached to the rope as the pivot. This gives us the following equation:

(135 kg)(9.81 m/s²)(3 m) + (mC)(9.81 m/s²)(6 m) - (150 kg)(9.81 m/s²)(4.5 m) - (1962 N)(3 m) = 0

Simplifying: (135)(3) + (6mC) - (150)(4.5) - (1962)(3) = 0

Rearranging: 6mC = 150(4.5) + 1962 - 135(3)

6mC = 2127

mC ≈ 196.2 kg

Therefore, the value that represents the mass of block C required to keep crate D in equilibrium is approximately 196.2 kg. Thus, the correct option is D.

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A Balloon is filled with water inside, when it is hanged over a burning fire the balloon filled with water doesn't brust why??​

Answers

because of the water buddy

technology is restricted to a single room or line of sight because this light spectrum cannot penetrate walls T/F

Answers

The statement ''Technology is restricted to a single room or line of sight because this light spectrum cannot penetrate walls'' is true because the restriction of technology to a single room or line of sight is typically due to the limitation of certain light spectrums, such as visible light or infrared, to penetrate walls.

These light spectrums are commonly used in technologies like remote controls, infrared sensors, or optical communication systems.

Visible light and infrared radiation have shorter wavelengths compared to radio waves, which allows them to carry more information.

However, their shorter wavelengths also make them more susceptible to absorption, reflection, or scattering by solid objects like walls. As a result, the range of these technologies is limited to the immediate vicinity or the line of sight between the transmitter and the receiver.

In contrast, radio waves, which have longer wavelengths, can penetrate walls and other obstacles more effectively.

This is why technologies like Wi-Fi, Bluetooth, and cellular networks that utilize radio waves have a broader coverage area and are not restricted to a single room or line of sight.

So, in summary, the statement is true that technology restricted to a single room or line of sight is due to the limitations of certain light spectrums, like visible light or infrared, to penetrate walls.

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Some ringtones for mobile phones can only be heard by young people. What is the likely frequency of these ringtones?
a. 250 Hz
b. 5,000 Hz
c. 10,000 Hz
d. 17,000 Hz​

Answers

Answer:

About 250 Hz

Explanation:

People of All ages without a hearing impairment should be able to hear the 8000hz. People under 50 should be able to hear the 12,000hz and people under 40, the 15,000hz. Under 30s should hear the 16,000hz, and the 17,000hz is receivable for those under 24.

Inertia is ______ to mass.

Answers

Answer:

Inertia is directly proportional to mass of an object. Therefore, when the force of inertia increases the mass also increases, and when it decreases the mass also decreases.

Explanation:

Answer: Inertia is _ directly proportional_ to mass.

Explanation:

If you have 100 kg of each of these substances, which would require the most energy to increase its temperature by 25 Kelvin?

A. Iron
B. Carbon
C. Rubber
D. Air

If you have 100 kg of each of these substances, which would require the most energy to increase its temperature

Answers

Answer:

iron

Explanation:

Explain how to get a positive electric charge ​

Answers

Answer:

An electrical charge is created when electrons are transferred to or removed from an object. Because electrons have a negative charge, when they are added to an object, it becomes negatively charged. When electrons are removed from an object, it becomes positively charged

A snail can move app approximately 0.30 inches per minute. How many meters can the snail cover in 15 minutes

Answers

4.5 i’m pretty sure sorry if i’m wrong

Answer:

4.5 because just do the math and its 4.5

Compared with a simple galvanometer, an electric motor is _____. A. The coil becomes a stronger electromagnet
B. Circle the wire in closed loops.
C. Much the same with small modifications
D. Similar to that of an interior bar magnet

Answers

Compared with a simple galvanometer, an electric motor is Much the same with small modifications.

ABOUT ELECTRIC MOTOR

An electric motor is a device for converting electrical energy into mechanical energy. A tool that functions the other way around, converting mechanical energy into electrical energy is called a generator or dynamo. Electric motors can be found in household appliances such as fans, washing machines, water pumps, vacuum cleaners. and much more.

Electric motors that are commonly used in the world Industry are asynchronous electric motors, with two global standards namely IEC and NEMA. metric (millimeter) based IEC asynchronous motors, while imperial  (inch) based NEMA electric motors, in applications there are power units in horsepower (hp) and kiloWatt (kW).

IEC electric motors are divided into several classes according to their efficiency, as a standard in the EU, this class division is EFF1, EFF2 and EFF3. EFF1 is the most efficient electric motor, consumes the least amount of energy, while EFF3 is no longer allowed to be used in the EU environment, because it wastes fuel in the power plant and will automatically generate the most carbon emissions, thus polluting the environment even more.

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this si a 2 part question84) A shock absorber is designed to quickly damp out the oscillations that a car would otherwise make because it is suspended on springs. (a) Find the period of oscillation of a 1610-kg car that is suspended by springs that make an effective force constant of 5.75×104 N/m. (b) Find the damping constant b that will reduce the amplitude of oscillations of this car by a factor of 5.00 within a time equal to half the period of oscillation.

Answers

Given data

*The given mass of the car is m = 1610 kg

*The given effective force constant is k = 5.75 × 10^4 N/m

(a)

The formula for the period of oscillation of a 1610 kg car is given as

\(T=2\pi\sqrt[]{\frac{m}{k}}\)

Substitute the known values in the above expression as

\(\begin{gathered} T=2\times3.14\times\sqrt[]{\frac{1610}{5.75\times10^4}} \\ =1.05\text{ s} \end{gathered}\)

Hence, the time period of oscillation of a 1610 kg car is T = 1.05 s

(b)

As from the given data, the amplitude of the oscillation of the car decreases by a factor of 5.00. Then, the expression for the amplitude of the oscillation, and the damping constant (b) is calculated as

\(A=A_0e^{-\frac{bt}{2m}}\)

Substitute the known values in the above expression as

\(\begin{gathered} \frac{A_0}{5.0}=A_0e^{-\frac{bt}{2m}} \\ bt=2m\ln (5.0)_{} \\ b(\frac{T}{2})=2m\ln (5.0) \\ b=\frac{4m\ln (5.0)}{T} \\ =\frac{4\times1610\times\ln (5.0)}{1.05} \\ =9871.2\text{ kg/s} \end{gathered}\)

Hence, the damping constant is b = 9871.2 kg/s

. philip is interested in knowing whether or not parental household income affects the maximum level of education achieved, so he sends out a questionnaire to 300 people in the triangle area. half come back to him and answered correctly. he analyzes the data and finds a correlation of +0.76.

Answers

Philip's analysis suggests a positive correlation (+0.76) between parental household income and the maximum level of education achieved.

Based on Philip's questionnaire and analysis, he found a correlation of +0.76 between parental household income and the maximum level of education achieved. This correlation suggests a positive relationship between these two variables.

To interpret this correlation, it means that as parental household income increases, there is a tendency for the maximum level of education achieved to also increase. However, it is important to note that correlation does not imply causation. This means that while there is a strong association between the two variables, it does not necessarily mean that parental household income directly causes higher education levels.

The fact that half of the 300 people who received the questionnaire answered correctly indicates that there was a 50% response rate. This information is useful to consider when generalizing the findings to the larger population.

It's important to acknowledge that this information is based on the specific sample Philip collected data from, and may not be representative of the entire population. To make more generalized conclusions, a larger and more diverse sample would be necessary.

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What is the unit of current and voltage?

Answers

Answer:

Explanation:

Current (I) is measured in amps (A)

Voltage (V) is measured in volts (V)

The volts is the measurement unit for voltage (V). The measurement unit for current is the ampere, and amp (A). the resistance unit of measurement, the ohm.

What unit does the current have?

The SI measure known as just an ampere, or A, is used to measure electric current. By presuming that the elemental charge, e, has a fixed real number of 1.602 176 634 10-19 when mostly expressed in unit C, which is actually equivalent to the seconds in terms of vCs, it is calculated.

The voltage measuring unit is what?

Volts are the units used to quantify electric potential difference, often known as voltage. A volt is defined as the difference in between two points on a cable that is carrying a current of just one ampere and releasing one watt of energy.

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In which state of matter, do the particles have the maximum energy?
A
Solid
B
Liquid
C
Gas
D
None of these

Answers

a solid ok thank you

hope it helps

The answer is C (Gas)

does food have energy?​

Answers

Answer:

Yes.

Explanation:

Food provides units of energy in the form of calories that give our bodies fuel to perform all functions from the most basic like breathing to more complicated activities. We need a minimum amount of calories from food to sustain basic metabolic functions and more to carry out physical activities. The more active we are, the more food we need.

Answer:

yes

Explanation:

because Our body uses energy for all of its functions and food is the main source of energy. Food contains nutrients that when broken down in the gastrointestinal tract release energy that can be used by the body's cells, tissues and organs for normal function, growth and repair.

A force of 5 N gives to mass my and an acceleration of 8m/s2 and a mass m2
an acceleration of 24m/s2. What acceleration would it give if both masses are
tied together

Answers

Answer:

a=6m/sec²

Explanation:

f=5 N

a1=8m/sec²

a2=24m/sec

m1=f/a1=5/8kg

m2=f/a2=5/24kg

New, f=(m1+m2)a

a=5/5/8+5/24=5/15+5/24=24*5/20

a=6m/sec²

Find the magnitudes of the horizontal and vertical components for the vector v, if α is the direction angle of v from the horizontal.α =166.4, |v| = 5171. The magnitude of the horizontal component of v is ___(Round to the nearest integer as needed.)2. The magnitude of the vertical component of v is ____(Round to the nearest integer as needed.)

Answers

The final answer is magnitude of the horizontal component of v is approximately 3662, and the magnitude of the vertical component of v is approximately 3396.

To find the magnitude of the horizontal and vertical components of a vector, we can use the trigonometric functions cosine and sine. The direction angle of the vector is given as 166.4°, which is the angle between the vector and the horizontal axis.

To find the horizontal component, we use the formula Horizontal Component = |v| * cos(α), where |v| is the magnitude of the vector and α is the direction angle. We substitute the given values and obtain:

Horizontal Component = 5171 * cos(166.4°) = 3662

To find the vertical component, we use the formula Vertical Component = |v| * sin(α), where |v| is the magnitude of the vector and α is the direction angle. We substitute the given values and obtain:

Vertical Component = 5171 * sin(166.4°) = 3396

Therefore, the magnitude of the horizontal component of v is approximately 3662, and the magnitude of the vertical component of v is approximately 3396.

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A covalent bond in which electrons are shared unequally is
a.
polar.
b.
a double bond.
c.
ionic.
d.
polyatomic.

Answers

Answer is A, hope this helps!

What happens to the pressure as air rises from the ground into the atmosphere?
Does it increase or decrease?

Answers

Answer:

please try brainlist answer

As the atmosphere expands the further you get from the Earth's surface, it becomes less dense and air pressure decreases. As you increase altitude (distance from Earth's surface) in an airplane, air pressure changes

कृपया ब्रेनलिस्ट का उत्तर केवल 1more उत्तर देने का प्रयास करें।

A ball of moist clay falls 17.3 m to the ground. It is in contact with the ground for 24.0 ms before stopping. (a) What is the average acceleration of

Answers

Answer:

Acceleration,  \(767.08\ m/s^2\)

Explanation:

Given that,

Height from a ball falls the ground, h = 17.3 m

It is in contact with the ground for 24.0 ms before stopping.

We need to find the average acceleration the ball during the time it is in contact with the ground.

Firstly, find the velocity when it reached the ground. So,

\(v^2=u^2+2ah\)

u = initial velocity=0 m/s

a = acceleration=g

\(v=\sqrt{2gh} \\\\v=\sqrt{2\times 9.8\times 17.3} \\\\v=18.41\ m/s\)

It is in negative direction, u = -18.41 m/s

Let a is average acceleration of the ball. Consider, v = and u = -18.41 m/s.

\(a=\dfrac{v-u}{t}\\\\a=\dfrac{0-18.41}{24\times 10^{-3}}\\\\a=767.08\ m/s^2\)

So, the average acceleration of the ball during the time it is in contact is \(767.08\ m/s^2\).

"Please include all relevant working out as detailed as possible
and all relevant diagram to find the answer. Much appreciated! I
will upvote! Thank you so much"
Find total response of the system (transient+steady state). Do not solve for coefficients. Determine the frequency of applied force at which resonance will occur? M = 20 kg F, = 90 N Given: -6 rad/s M

Answers

Given the following information:Mass of the system, m = 20 kg.Damping coefficient, b = 6 Ns/m.Force, F = 90 N.Frequency of applied force, f = ?Applied force angular frequency, w = 6 rad/s.Forced vibration equation:F(t) = F0 sin(wt)where F0 = 90 N and w = 6 rad/s.Under the action of the force F, the mass m will oscillate.The equation of motion for the mass-spring-damper system is given by:$$\mathrm{m\frac{d^{2}x}{dt^{2}}} + \mathrm{b\frac{dx}{dt}} + \mathrm{kx = F_{0}sin(\omega t)}$$where k is the spring constant.x(0) = 0 and x'(0) = 0.As we have the damping coefficient (b), we can calculate the damping ratio (ζ) and natural frequency (ωn) of the system.Damping ratio:$$\mathrm{\zeta = \frac{b}{2\sqrt{km}}}$$where k is the spring constant and m is the mass of the system.Natural frequency:$$\mathrm{\omega_{n} = \sqrt{\frac{k}{m}}}$$where k is the spring constant and m is the mass of the system.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$At resonance, the amplitude of the system will be maximum when forced by a sinusoidal force of frequency equal to the resonant frequency.Resonant frequency:$$\mathrm{\omega_{d} = \sqrt{\omega_{n}^{2}-\zeta^{2}\omega_{n}^{2}}}$$$$\mathrm{\omega_{d} = \sqrt{(6.57)^{2}-(-2.88)^{2}} = 6.98 rad/s}$$Hence, the frequency of applied force at which resonance will occur is 6.98 rad/s.

The frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

To determine the frequency of the applied force at which resonance will occur, resonance happens when the frequency of the applied force matches the natural frequency of the system. The natural frequency can be determined using the formula:

ωn = √(K / M),

where ωn is the natural frequency, K is the spring constant, and M is the mass of the system.

Substituting the given values of K = 400 N/m and M = 20 kg into the equation, we can calculate the natural frequency ωn.

ωn = √(400 N/m / 20 kg) = √(20 rad/s²) = 2√5 rad/s.

Therefore, the frequency of the applied force at which resonance will occur is ω = 2√5 rad/s.

The correct question is given as,

M= 20kg

Fo = 90 N

ω = 6 rad/s

K = 400 N/m

C = 125 Ns/m

Determine the frequency of applied force at which resonance will occur?

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The burning of a log releases the logs chemical_energy into other forms of energy

Answers

Answer:

When we burn wood we are releasing solar energy, in the form of heat, that has been stored in the wood as chemical energy. The process of photosynthesis converted solar energy, water and carbon dioxide into oxygen and the organic molecules that form the wood, half the weight of which is carbon.

Explanation:

A spring (k= 100 N/m) that is initially compressed launches a solid small toy ball of mass 0.250 kg from rest along a horizontal surface as shown. the ball does not slip ( meaning it is moving to the right and also rolling) as it moves to the right. If the balls final linear speed is 6.8 m/s find the initial compression distance of the spring

A spring (k= 100 N/m) that is initially compressed launches a solid small toy ball of mass 0.250 kg from

Answers

Given data:

The mass of the ball is m=0.25 kg.

The spring constant is k=100 N/m.

The speed of the ball is v=6.8 m/s.

The amount of energy stored in the spring in the form of elastic potential energy will equal to the kinetic energy of the ball. It can be applied as,

\(\begin{gathered} PE=KE \\ \frac{1}{2}kx^2=\frac{1}{2}mv^2 \end{gathered}\)

Here, x is the compression in the spring.

Substitute the given values in above equation,

\(\begin{gathered} \frac{1}{2}(100)x^2=\frac{1}{2}(0.25)(6.8)^2 \\ x=0.34\text{ m} \end{gathered}\)

Thus, the initial compression of the spring is 0.34 m.

A block of unknown object has the measurements of 5-cm by 2-cm by 3-cm What is the density of the unknown object?

Answers

Answer:

volume = 30cm^3

Explanation:

An airplane is traveling 200 mph south. You get up and walk down the aisle at 1 mph north. Your resultant velocity is

Answers

199 mph south
using the formula 200 - 1 = 199 mph south

Which of the following best demonstrates Newton's Third Law?
Question 3 options:

The harder you kick a soccer ball, the faster it accelerates

An object sitting on the ground will stay there until somebody or something pushes it

Wearing a seatbelt prevents you from continuing to move when the car has stopped

When you walk your foot pushes down on the ground while the ground pushes back on your foot

Answers

Answer:

when you walk your foot pushes down on the ground, while the ground pushes back on your foot

Explanation:

it was another brainly question, Goodluck :)

It’s the third option

WILL MARK BRAINLIEST!!
Select ALL that are true of acceleration.

A change in speed will result in a change in acceleration.

Decreasing acceleration is also called deceleration.

A decrease in speed will result in change in acceleration.

Constant acceleration is constantly changing.

Answers

None of the statements are true except for "Decreasing acceleration is also called deceleration."

Acceleration is the rate of change of velocity, so it involves a change in velocity over time.
A change in speed will result in a change in acceleration, but not necessarily in the same direction.
A decrease in speed will result in a change in acceleration, but the acceleration will be in the opposite direction of the initial velocity.
Constant acceleration means that the acceleration is not changing, so it is not constantly changing.

I hope this helps :)

A change in speed is acceleration ... it can be constant or changing.

Decreasing acceleration is also called deceleration. No.

A decrease in speed is acceleration ... it an be constant or changing.

Constant acceleration is constantly changing. No.


What is the frequency of a wave with a wavelength of 15 m and a wavespeed of
300 m/s?

Answers

Answer: f=20 (i think)

Explanation:

all I did was divide 300 and 15.

300/15= 20

Which one best represents the heat capacity of a system represented by identical quantum harmonic oscillators?

Answers

Even when we don't know its exact location, a classical particle has a specific position at a specific moment. For a quantum particle, this is no longer valid. The probability densities and energy eigenfunctions for the quantum oscillator go over the boundaries of the conventional turning points.

The analog of the classical harmonic oscillator in quantum mechanics is called the quantum harmonic oscillator. One of the most crucial model systems in quantum mechanics is the arbitrary smooth potential, which is one of the most common ways that a smooth potential can be represented as a harmonic potential at a stable equilibrium point. It is referred to as "harmonic" because the solution of Newton's second law, a second-order differential equation that governs the motion of the item, is a series of sines and cosines of time with a specific frequency, exactly like the outcome.

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Gravitational potential energy is the energy stored in an object due to its height
above a reference level. Which of the following choices best describes the
correct formula of gravitational potential energy?

Gravitational potential energy is the energy stored in an object due to its heightabove a reference level.

Answers

ΔU = mgh is the expression to Gravitational Potential Energy for Height (h).

What kind of energy from gravitational potential is that?

A book on even a high shelf, for instance, has more energy potential than a book here on bottom shelf since it requires a longer distance to fall. Items having gravitational potential energy can also include the following: a heavier burden. water retentive to a dam.

Why does kinetic energy differ from gravitational potential energy?

The energy held within an item as a result of its height above the ground is known as gravitational potential energy. The object's height, gravitational acceleration caused by the Earth, and mass all play a role in this. The energy an item possesses as a result of its motion is known as kinetic energy.

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the drawing shows an exaggerated view of a rifle that has been"sighted in" for a 91.4-meter target. If the muzzle speed of thebullet is v0 = 427 m/s, what are the two possible anglesθ1 and θ2 between the rifle barreland the horizontal such that the bullet will hit the target? One ofthese angles is so large that it is never used in target shooting.(HInt: the following trigonometric identity may be useful: 2 sinθ cos θ = sin 2 θ.)

Answers

The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

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The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

to learn more about displacement.

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