the fundamental frequency is 300 Hz is the answer.
Constructive Frequency
Peak frequency differences are different by
= 1200 - 900 = 900 - 600 = 300 Hz
hence, the fundamental frequency is 300 Hz.
Since the frequency of constructive interference is an integer multiple of the fundamental frequency, the fundamental frequency can be calculated from the difference between two successive peak frequencies.
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A sports car accelerates at a constant rate from rest to a speed of 27. 8 m/s in 8. 00 s. What is the displacement of the sports car in this time interval?.
The displacement of the sports car is approximately 222.4 m. This is the distance traveled by the car in the 8.00 s time interval, assuming that it accelerates at a constant rate.
To calculate the displacement of the sports car, you will need to know its acceleration as well as its initial and final velocities. Displacement is defined as the change in position of an object, and it can be calculated using the equation:
Displacement = (Final Velocity + Initial Velocity) / 2 * Time
In this case, the initial velocity of the sports car is 0 m/s (since it is starting from rest) and the final velocity is 27.8 m/s. The time interval is 8.00 s. Plugging these values into the equation above, we get:
Displacement = (27.8 m/s + 0 m/s) / 2 * 8.00 s
This simplifies to:
Displacement = 27.8 m/s / 2 * 8.00 s
This further simplifies to:
Displacement = 27.8 m/s * 8.00 s / 2
This simplifies to:
Displacement = 222.4 m
So the displacement of the sports car is approximately 222.4 m. This is the distance traveled by the car in the 8.00 s time interval, assuming that it accelerates at a constant rate.
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What does the subscript 2 indicate in br2?
The subscript 2 in [tex]Br_2[/tex] indicates that two atoms of bromine are joined together.
[tex]Br_2[/tex], which is a bromine compound, is formed by the combination of two bromine atoms.
At normal temperature and pressure, the original colour of Bromine ([tex]Br_2[/tex]) is a red-brown liquid.
When there is a subscript "2," it signifies that a molecule is made up of two Bromine atoms.
We never use subscripts of "1" while writing the chemical formula, since they are only used when more than one atom is being represented.
When referring to a diatomic molecule, we use the element's symbol and add the subscript "2" to denote the bond between two of that element's atoms.
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What are the 3 main causes of CO2 emission?
The primary global sources for carbon dioxide emissions are electricity and heating (31%) as well as farming (11%), transportation (15%), forestry (6%) and manufacturing (12%).
Which three things cause carbon dioxide emissions?These sources can be found primarily in three different contexts: industrial processes, natural gas processing, and fuel combustion activities.By far, burning fossil fuels causes carbon to oxidize, which is what causes the biggest CO2 emissions.
What are the four main sources of carbon?The combustion of fossil fuels including gas, coal, and oil, deforestation, and volcanic eruptions are a few examples of carbon sources.
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How does the mass of the sodium metal and chlorine gas involved in the reaction, compare to the mass of the table salt produced?.
According to the law of conservation of mass, the total mass of reactants and products in a chemical reaction is equal.
In a chemical process, the total mass of the reactants will be much smaller than the total mass of the products. A. Sodium metal and chlorine gas combine to generate sodium chloride in the chemical reaction shown below. will be 100 grammes exactly.
Chlorine gas and sodium metal combine to form sodium chloride (table salt) The mass of sodium chloride generated when the reaction is finished will be exactly 100 grammes if the combined mass of the reactants is 50 grammes.
A sodium cation (Na+) and a chloride anion are created when a sodium atom transfers an electron to a chlorine atom.
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What does the N stand for in this formula?
The total number of subjects or observations in the sample is denoted by the letter "n."
What does math's N stand for?The collection of all natural numbers is known as N. Positive, non-zero whole numbers make up the natural numbers. N = 1 , 2 , 3 , 4 , .
What does N in a series represent?The letter "n" represents the word "number." By changing the term number's value, we can create a sequence utilizing the nth term ( n ). Following the sequence's formula, we would substitute 10 for "n" to obtain the 10th term; similarly, we would substitute 50 for "n" to discover the 50th term.
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What are authorized sources for derivative classification?
An existing, correctly designated source document that has been extracted, rephrased, restated, and/or generated in a new form for inclusion in another document counts as a second permitted source for derivative classification.
Who is eligible to serve as an initial classification authority?the OCA rollover Classification Authority at Origin a person appointed in writing to classify material in the first instance by the President, the Vice-President, agency heads, or other president-designated officials.
What information is contained in the block containing the categorization authority?The classification authority block, or CAB, indicates who has power over and how long the classification determination will last. It identifies the person who classified the document, what it was generated from, what it was downgraded to (if applicable), and the date it was declassified.
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How do you find nSolve?
You may get approximate numerical values for each of a polynomial equation's roots with NSolve. NSolve can be used to solve groups of concurrent equations. Mathematica's numerical mathematics (Mathematica Tutorial)
Describe NSolve.Equation, "Variable = initial value," NSolve identifies numerically all possible answers to the given equation for the provided unknown variable and its initial value.
What makes solve and NSolve different from one another?To solve an equation or group of equations algebraically, use the function solve. Although it is sometimes preferable to have a numerical solution, it is not always possible to solve an equation algebraically. In either scenario, a group of equations or an individual equation can be solved numerically using NSolve.
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What is the process of splitting light called?
The dispersion of white light into its various colors is referred to as dispersion. Due to the medium's refraction property, each wavelength moves through the medium at a different pace, producing this property.
What is the term for the splitting of light?Dispersion is the name for the process through which visible light separates into its individual colors.
What splits the light, and why?We have seen that when white light is transmitted through a glass prism, it is scattered into the spectrum of colors that make up white light. Therefore, we can observe that the phenomena of light separating into its individual hues is called dispersion of light.
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What are the 15 categories of Scope 3 emissions?
Scope 3 Purchased goods and services, capital goods, fuel- and power activities, transportation and distribution, waste produced throughout operations, business trips, employee commuting, leased assets, processing of sold goods, use of sold goods, end-of-life treatment of sold goods, franchises, and investments are just a few of the three emission categories.
There are how many separate Scope 3 emission categories?twenty groups Although not all businesses would fit into every category, the GHG Protocol defines 15 classifications for scope 3 emission. Upstream and downstream of a organization's operations are both considered sources of emissions within Scope 3.
Which emission categories are there?Explained: emission types 1, 2, and 3.The primary GHG Protocol business standard divides a firm's greenhouse gas emissions into three categories. While reporting for scopes 1 and 2 is required, monitoring for scope 3 is optional and more difficult.
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What are the 7 wavelengths?
They are: radio waves, microwaves, ir, visible, ultraviolet, x-rays, and gamma rays.
Which order do the seven wavelengths go in?The following list of the seven electromagnetic waves is organized by decreasing wavelength & increasing frequency and energy:X-rays, gamma rays, UV rays, visible light, radio waves, microwaves, and infrared waves.
What kinds of wavelengths are there?Typically, electromagnetic radiation is divided in radio wave, microwave, ir, visible light, ultraviolet, X-rays, and gamma rays categories based on its wavelength.
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Why is it important to have a reference direction specified before describing a location in terms of positive or negative?n
It is important to have a reference direction specified before describing a location in terms of positive or negative because that reference point is the 0 Value of the distance we are going to describe in Negative or positive direction as that direction is given according to the point 0.
What is direction?Direction is the path given from a reference point telling that how much something travelled or developed in a specific position.
Reference point:
It is the fixed point from where soemithin is defined is respect with that reference point. As example the distance of Suraj from Reeta is 2 km here Reeta is reference point.To know more about Direction visit
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objects x and y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, creating an atwood’s machine, as shown in the figure. the objects are initially at rest, and the mass of object y is greater than the mass of object x. as object y falls, how does the kinetic energy of the center of mass of the two-object system change? justify your selection. all frictional forces are considered to be negligible.
The kinetic energy increases because the gravitational force due to Earth does positive net work on the system.
What is law of conservation of energy?Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another.
When objects x and y are connected by a string of negligible mass and suspended vertically over a pulley of negligible mass, the system stored gravitational potential energy. When object y falls, this potential energy changes into kinetic energy.
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a worker drives a .500 kg spike into a rail tie with a 2.50 kg sledgehammer. the hammer hits the spike with a speed of 65 m/s. if one third of the hammers kinetic energy is converted to the internal energy of the hammer and spike how much does the total internal energy increase?
dang, someone help me and explain this pleasseeee!!
Answer:
Explanation:
To find the increase in total internal energy, we first need to find the kinetic energy of the sledgehammer before it hits the spike. We can use the formula:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
Plugging in the values, we get:
KE = (1/2) * 2.50 kg * (65 m/s)^2
KE = (1/2) * 2.50 kg * 4225 m^2/s^2
KE = 5212.5 J
Next, we need to find the amount of energy that is converted to internal energy. Since one third of the kinetic energy is converted to internal energy, we can multiply the kinetic energy by 1/3 to find this value:
E = 1/3 * 5212.5 J
E = 1737.5 J
Finally, we need to find the total internal energy increase by adding the energy converted to internal energy to the initial internal energy of the hammer and spike. Since the initial internal energy is zero, the total internal energy increase is simply the energy converted to internal energy:
Total internal energy increase = 1737.5 J
Therefore, the total internal energy increases by 1737.5 J when the sledgehammer hits the spike.
The length of the minute hand of the wall clock is 10 cm. How far will the endpoint of this pointer travel in 2 hours?
please help me
The length of the minute hand of a wall clock is not relevant to finding the distance traveled by the end of the pointer in a given amount of time. The only important factors are the length of the hour hand and the amount of time that has passed.
If the length of the hour hand is X cm, then the distance traveled by the end of the pointer in 2 hours can be calculated as follows:
Distance traveled = (X * π * 2) cm
Here, π is the mathematical constant approximately equal to 3.14. The factor of 2 in the formula represents the number of hours that have passed. Therefore, to find the distance traveled in 2 hours, you would need to know the length of the hour hand and substitute it for X in the formula above.
here is a thumb dipped in paint
which of the following of the ripe fruits is around the same size as the coloured part of the thumb
a. strawberry and mango
b lemon and orange
c grape and cherry
d lychee and apple
The ripe fruits is around the same size as the colored part of the thumb are grape and cherry. Hence, option (C) is correct.
What is fruit?Fruit is a blooming plant's fleshy or dry, fully developed ovary that contains a seed or seeds. As a result, apricots, bananas, and grapes are all considered to be fruits as well as bean pods, maize grains, tomatoes, cucumbers, and (in their shells) acorns and almonds. However, the term is typically only used to describe matured ovaries that are delicious and either pulpy or succulent.
A developed ovary and its related elements constitute a fruit in terms of botany. It often contains seeds that have grown from the encased ovule after fertilization, though parthenocarpy, or growth without fertilization, is also known.
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How is ultrasound used to detect the depth of the sea?
A SONAR transmits ultrasonic waves into the ocean, and after two seconds, it detects the reflected waves from a sunken ship.
How do we measure the depth of the ocean?
The scanning sonar concurrently produces ultrasonic waves 360 degrees around the ship and is able to rapidly recognise and display any echoes that do return.
Sound is frequently and quickly used to determine ocean depth. Ships can scan the terrain of the ocean below using a technology known as sonar, which stands for sound navigation and range. The device sends sound waves to the ocean floor and measures how long it takes for an echo to return. An ocean depth gauge is called a fathometer.
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What is operant conditioning vs classical conditioning?
Its consequences, either rewarding the desired behavior or punishing the undesired behavior. It is based on the idea that behavior is a function of its consequences. modified by the association of a stimulus with a previously neutral stimulus. It is based on the idea that behavior is a function of its antecedents.
Operant conditioning is a type of learning in which an individual's behavior is modified by its consequences. It is based on the idea that behavior is a function of its consequences, either rewarding the desired behavior or punishing the undesired behavior in order to shape behavior. Classical conditioning is a type of learning in which an individual's behavior is modified by the association of a previously neutral stimulus with a particular stimulus. It is based on the idea that behavior is a function of its antecedents. In operant conditioning, the response is voluntary, while in classical conditioning, the response is involuntary. Operant conditioning focuses on how behavior is strengthened or weakened in response to reinforcement or punishment, while classical conditioning focuses on how behavior is acquired through association.
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The maximum speed around a level curve is 30. 0 km/h. What is the maximum speed around a curve with twice the radius? (assume all other factors remain unchanged. ).
The maximum speed around a level curve is 30. 0 km/h. What is the maximum speed around a curve with twice the radius is 42.4 km/h.
Meaning of the maximum speed curve:
You might travel at a maximum speed of around 1.4 times as fast on a curve with a radius of 60 meters (twice as much), according to the equation, which also states that your maximum speed is proportional to the square root of the curve's radius.
According to that,
30 km/hr is the maximum speed.
New radius equals 2 r
In all scenarios, the centripetal force will be the same.
Calculating the new top speed around a curve is necessary.
Using the centripetal force formula:
[tex]\frac{mv^{2} }{r} = \frac{mv^{2}}{r}[/tex]
Fill out the formula with the value
[tex]\frac{v^{2} }{2r} = \frac{30^{2} }{2r}[/tex]
[tex]v= 30\sqrt{2} \ Km/h[/tex]
[tex]v = 42.4 Km/h[/tex]The maximum speed around a curve is therefore 42.4 km/h.
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Immediately after they push away from each other, how does the motion of the mother and daughter change?.
Both travel rearward, but the daughter accelerates more quickly motion.
Every action has an equal and opposite response, according to Newton's third law of motion. Consequently, when the two skaters collide. They'll both advance backward together.
However, the mother weighs 100 kg, compared to the daughter's 50 kg. due to the daughter's lower mass. Daughter as a result accelerates more quickly in the reverse direction.
As a result, both travel backward, but the daughter does so more quickly than the mothe motionr.
The following is an expression that represents Newton's second law:
a = F/m and F = ma or
According to this law, a body's acceleration is determined by two variables. The first is the body's mass and the net force that is operating on it. The acceleration is directly proportional to the net force acting on the body and inversely proportional to the mass.
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what characteristic of the air track is important to this experiment? the air track blows air to maximize friction so that the cart motion is one-dimensional. the air track provides air flow to support the frictionless rotation of the pulley. the air track has low friction with the carts so that non-conservative forces (such as friction) are minimized. the air track is massless so that the motion of the track does not affect our measurement.
An experimental tool known as an air track enables the investigation of motion with the least amount of frictional disturbance. It is made out of a track with several tiny holes through which air is constantly blown.
What purpose does air track serve?A scientific tool called an air track is used to investigate motion in a low-friction setting. Its name is derived from the way it is built: air is pumped through a hollow track with tiny holes spaced out along the track to allow specially designed air track cars to float along with little resistance.
Why is it critical to level the air track before doing the experiment?It will be required to level the air-track as carefully as possible in order to examine motion with constant velocity.
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the w10×15 cantilevered beam is made of a-36 steel and is subjected to the loading shown.(figure 1)
A-36 steel is used to construct the w10x15 cantilevered beam, which is put under the indicated loading.
Moment of inertia for w10×15 is equal to 68.9in4 and Young's modulus for A–36 steel is equal to 29e3 ksi. Thus Slope at B can be given as,
θB = P₂x³/ (2EI) + P₁l³/ (2EI)
θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)
θB = 0.0042rad
Therefore , displacement at B can be written as,
yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)
yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)
yB = 0.034ft
The given question is incomplete,
The W10×15 cantilevered beam is made of A-36 steel and is subjected to the loading shown. Suppose that w = 2.7 kip/ft .E = 29 (103) ksi and I = 68.9 in4. (Figure 1) Determine the slope of the beam B, measured counterclockwise from the positive x axis. Determine the displacement of the beam at B.
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some give me atleast 5
Robot Mass stays the same. Anywhere in the universe, an object has the same mass as it has on Earth. Gravity affects an object's weight. The identical object weighs less on the moon than it does on Earth because there is less gravity there.
What mass of robot on moon and earth?The mass and size of the moon also impact its gravitational pull. The moon won't draw things toward itself with the same force as the Earth because it has a lot less mass than the latter.
Therefore, This implies that even if robot mass remains the same, you would weigh less if you traveled to the moon.
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A ladybug is crawling up a wall at constant speed, as shown above. Which of the following are correct justifications for how forces help the ladybug move up the wall? Select two answers
A constant nonzero net force acts on the ladybug as it moves up the wall.
The ladybug exerts a downward force on the wall to move itself up the wall.
The upward force of the wall on the ladybug moves the ladybug up the wall.
The ladybug exerts an upward force on itself to move it up the wall.
A downward force is applied by the ladybug to the wall in order to advance up the wall, and a vertical force is applied by the wall to the ladybug.
What are the different kinds of force?The definition of force is the power or fuel applied to an item during any positive exercise or movement. A pressure or pull that results from two objects interacting is called a force. External force doesn't actually exist until two objects interact.
Why is force such a big deal?Forces are important because they produce changes to motion, as we learned in a prior lesson. Isaac Newton actually cites this in his first law. This inertia concept describes the phases of stillness and motion that occur in the absence of an external, opposing force.
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please can any one answer for this question
Answer:
S = 1/2 g t^2 time for stone to fall distance S
S = V0 (t - 2) * 1/2 g (t -2)^2 time for stone to fall distance S with an initial speed of 30 m/s, 2 seconds later
1/2 g t^2 = V0 t - 2 V0 + 1/2 g t^2 - 2 g t + 2 g equating distance fallen
t = 3.88 sec
Check:
S = 1/2 * 9.8 * 3.88^2 = 73.8 m
S = 30 * 1.88 + 1/2 * 9.8 * 1.88^2 = 73.7 m
your electric utility company sends you a monthly bill informing you of the number of kilowatt- hours you have used that month. a. is the utility charging you for energy or power? explain.
Your electric utility company sends you a monthly bill informing you of the number of kilowatt- hours you have used that month therefore the utility is charging you for energy.
What is a Utility?This is referred to as a type of service such as light, power etc which are provided by a public utility.
Electricity utility send us a monthly bill of the number of unit consumed by our appliance per month and the amount you owe is derived by multiplying your utility's rate per kWh by the total kWhs you used that month. It is also how much energy is used over a certain time period which is therefore the reason why energy was chosen as the correct choice.
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how can i run my car heater at maximum setting to cool down the engine if the car is overheated and the engine is stalled and just cranks without starting?
An engine can be cool down by the below steps
Leave the radiator cap on until it is coolPop the hood when there is no more steam coming out.Knowing how to cool an overheated engine is a significant expertise for any authorized driver. Having the option to analyze and fix your own issues can get you back out and about rapidly, forestall exorbitant mechanical issues, and assist you with realizing when to look for proficient assistance.
Steps which I can take to cool down an overheated engine of car:
The strain and steam inside can shoot a hazardous fly of liquid back at your face. Avoid any and all risks and leave the radiator cap on the vehicle however long you can. Assuming it feels warm to the touch, leave it.In the event that the vehicle isn't excessively hot, switch off the vehicle and pop your hood. Assuming the hood is incredibly hot to the touch or on the other hand on the off chance that you see steam, it is prudent to hold on until the hood cools before you open it as far as possible. Opening the hood disperses a portion of the intensity away from the motor.To know more about engine,visit here:
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If a net horizontal force of 8. 2 n is applied to a baby carriage whose mass is 11. 5 kg what acceleration is produced?.
Answer:
Below
Explanation:
F = m * a
8.2 N = 11.5 kg * a
a = .71 m/s^2
Let's try to do this math ourselves from this point. Notice how the s2 term in the acceleration (5 m/s2) and the s term in the time (7 s) cancel leaving you with m/s (velocity).
122 m/s
244 m/s
8.7 m/s
35 m/s
As per the given statement the s2 term in the acceleration (5 m/s2) and the s term in the time (7 s) cancel leaving you with 35 m/s (velocity).
What is velocity?Velocity is the rate of change of speed per unit time. It also determines the direction of the movement of object or moving body. hence, it is called as directional speed.
In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.v=Δx/Δt where v= average velocity, Δx=displacement, Δt=change in time.To know more about velocity visit
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What is cutoff frequency formula?
The cutoff frequency formula is 1 / (2 * pi * R * C).
What do you mean by cutoff frequency of a device?
The cutoff frequency of a device or system is the frequency at which its response starts to fall off sharply. It is the frequency above which the device or system does not pass or amplify signals effectively.
The cutoff frequency of a device or system can be calculated using the following formula:
cutoff frequency = 1 / (2 * pi * R * C)
where R is the resistance of the device or system, and C is the capacitance of the device or system.
The cutoff frequency is often used to describe the performance of electronic filters, such as low-pass filters, high-pass filters, and band-pass filters. It is also used to describe the performance of other types of systems, such as microphones and speakers.
Therefore, the cutoff frequency is formula is 1 / (2 * pi * R * C).
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A projectile is launched at 30° above ground level. what other angle at the same speed will result in the same range?
Answer:
[tex]60^{\circ}[/tex] (assuming that air resistance is negligible.)
Explanation:
Let [tex]g[/tex] denote the gravitational field strength. If air resistance on the projectile is negligible:
Vertical acceleration of the projectile will be constantly [tex](-g)[/tex]. In other words, [tex]a_{y} = (-g)[/tex].Horizontal velocity of the projectile will be constant.Let [tex]\theta[/tex] denote the angle at which the projectile is launched. Let [tex]v[/tex] denote the initial velocity of the projectile:
Initial vertical velocity of the projectile will be [tex]u_{y} = v\, \sin(\theta)[/tex].Initial horizontal velocity of the projectile will be [tex]u_{x} = v\, \cos(\theta)[/tex].Also because air resistance is negligible, vertical velocity of the projectile will be [tex]v_{y} = (-u_{y}) = (-v\, \sin(\theta))[/tex] right before the projectile lands. In other words, while the projectile was in the air, the change in vertical velocity would be [tex](-v\, \sin(\theta)) - (v\, \sin(\theta)) = (-2\, v\, \sin(\theta))[/tex].
Divide the change in velocity by acceleration to find the duration of the flight:
[tex]\begin{aligned}t &= \frac{v_{y} - u_{y}}{a_{y}} \\ &= \frac{(-v\, \sin(\theta)) - (v\, \sin(\theta))}{(-g)} \\ &= \frac{(-2\, v\, \sin(\theta))}{(-g)} \\ &= \frac{2\, v\, \sin(\theta)}{g}\end{aligned}[/tex].
Range measures the horizontal distance that this projectile has travelled. At a constant horizontal velocity of [tex]u_{x} = v\, \cos(\theta)[/tex], this projectile would travel a distance of:
[tex]\begin{aligned}(\text{range}) &= u_{x}\, t \\ &= (v\, \cos(\theta))\left(\frac{2\, v\, \sin(\theta)}{g}\right) \\ &= \frac{2\, v^{2}\, \sin(\theta)\, \cos(\theta)}{g}\end{aligned}[/tex].
Apply the double angle identity [tex]2\, \sin(\theta) \, \cos(\theta) = \sin(2\, \theta)[/tex] to further simplify this expression:
[tex]\begin{aligned}(\text{range}) &= \cdots \\ &= \frac{2\, v^{2}\, \sin(\theta)\, \cos(\theta)}{g} \\ &= \frac{v^{2}\, (2\, \sin(\theta)\, \cos(\theta))}{g} \\ &= \frac{v^{2}\, \sin(2\, \theta)}{g}\end{aligned}[/tex].
Note that in this question, [tex]v^{2}[/tex] and [tex]g[/tex] are both constant. Hence, for another angle of elevation [tex]\hat{\theta}[/tex], the range of the projectile will be the same as long as [tex]\sin(2\, \hat{\theta}) = \sin(2\, \theta)[/tex].
[tex]\sin(2\, \hat{\theta}) = \sin(2\, (30^{\circ}))[/tex].
Since [tex]0^{\circ} \le \hat{\theta} \le 90^{\circ}[/tex], [tex]0^{\circ} \le 2\, \hat{\theta} \le 180^{\circ}[/tex]:
[tex]\sin(2\, \hat{\theta}) = \sin(180^{\circ} - 2\, \hat{\theta}) = \sin(2\, (90^{\circ} - \hat{\theta}))[/tex].
Therefore, [tex]\hat{\theta} = 90^{\circ} - \theta = 90^{\circ} - 30^{\circ} = 60^{\circ}[/tex] will ensure that [tex]\sin(2\, \hat{\theta}) = \sin(2\, \theta)[/tex]. Launching the projectile at [tex]60^{\circ}[/tex] will reach the same range.
[tex]\begin{aligned}(\text{new range}) &= \frac{v^{2}\, \sin(2\, (60^{\circ}))}{g} \\ &= \frac{v^{2}\, \sin(2\, (30^{\circ}))}{g} = (\text{original range})\end{aligned}[/tex].