According to Maslow, self-actualization, the highest level of need, can only be achieved through satisfactory relations with others, emphasizing the importance of social connections in personal growth.
In Maslow's hierarchy of needs, self-actualization is the highest level of need, and it represents the individual's desire to reach their full potential and become the best version of themselves. Maslow believed that self-actualization could only be achieved after all other needs, including physiological needs, safety needs, belonging and love needs, and esteem needs, had been fulfilled.
Moreover, Maslow believed that self-actualization was closely tied to social relationships and interactions. He suggested that individuals must have positive and fulfilling relationships with others to reach their full potential and achieve self-actualization.
He also argued that people who lacked supportive relationships and social interactions were more likely to experience difficulties in achieving self-actualization.
Therefore, Maslow emphasized the importance of social connections and relationships in human well-being and personal growth.
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What is the elastic potential energy of a rubber band with a spring constant of 25.0 N/m if it is stretched by 10.0 cm from its original length?
Answer: 1,250 joules
Explanation: elastic potential energy is half of the spring constant multipied by extention squared so its 12.5 multiplied by 100 which is 1,250
which requires more work--lifting a 50- kg sack vertically 2 m or lifting a 25- kg sack vertically 4 m ?
The 50 kg sack and 25 kg sack requires same amount of work done to be lifted to the heights specified.
Let us calculate the work in lifting each sack.
Work done in lifting 50 kg is,
Mass m is given as 50 kg.
Height h = 2 m.
Acceleration due to gravity g = 9.8 m/s²
Work done is given by the formula,
W = m g h = 50× 9.8 ×2 = 980 J
Work done in lifting 25 kg is,
Mass m is given as 25 kg.
Height h = 4 m.
Acceleration due to gravity g = 9.8 m/s²
W = 25 × 9.8 ×4 = 980 J
Thus, it is observed that equal amount of work is needed to lift both the sacks.
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If a copper metal of diameter 5cm and length 1m is stuck into the base of a hot water bath such that the heat of the water at 80° Celsius is transmitted to the other end. calculate :
(1) the temperature gradient
(2) the quantity of heat supplied ( Take thermal conductivity of aluminium to be 386W/mk), if the temperature at the other end is 30° Celsius
Answer:
If a copper metal of diameter 5cm and length 1m is stuck into the base of a hot water bath such that the heat of the water at 80° Celsius is transmitted to the other end. calculate :
(1) the temperature gradient
(2) the quantity of heat supplied ( Take thermal conductivity of aluminium to be 386W/mk), if the temperature at the other end is 30° Celsius
Answer: The temperature gradient:
Explanation: ∇=T/L=80/1=80°C/m.
What is the magnitude of the average force (in kN) exerted on the pile driver by the I-beam while the two are in contact
To determine the magnitude of the average force exerted on the pile driver by the I-beam while they are in contact, additional information is needed.
The magnitude of the average force can be calculated using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = ma.
However, to determine the acceleration, more information about the motion or interaction is necessary. For example, if the pile driver and the I-beam are at rest and experience a sudden impact, the acceleration can be calculated using the formula for impulse: FΔt = mΔv, where F is the average force, Δt is the duration of contact, m is the mass of the pile driver, and Δv is the change in velocity.
Without additional information about the specific circumstances of the interaction between the pile driver and the I-beam, it is not possible to determine the magnitude of the average force accurately.
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Question 2: What is the velocity ratio of this pulley?
Load
distance=12 m
Effort
distance= 4 m
Answer:
1/3
Explanation:
Velocity ratio = distance moved by effort / distance moved by load
The A has a mean lifetime of 26 10-10s and decays into p + e- + ve with a branching fraction of 83 10-4. The A+ (udc) has a mean lifetime of 2-1 10-13s. Estimate the branching fraction of the A into A+e+ +ve, comment on how your result compares with the measured value. [m()=2285GeV/c2BR(e+ve)=(2106)%]
The mean lifetime of A is given by τ(A) = 26 × 10⁻¹⁰ s. The A decays into p + e⁻ + ve with a branching fraction of BR(A → p + e⁻ + ve) = 83 × 10⁻⁴.The mean lifetime of A⁺ (udc) is given by τ(A⁺) = 2-1 × 10⁻¹³ s.
The branching fraction of A into A⁺ + e⁺ + ve is given as follows: First, we can calculate the decay constant for A.λ = (1/τ) = (1/26 × 10⁻¹⁰) s⁻¹.The half-life of A is given by t₁/₂ = ln(2) / λ = (ln2 × τ) = 2.667 × 10⁻¹⁰ s. The branching fraction of A → A⁺ + e⁺ + ve is given as follows: BR(A → A⁺ + e⁺ + ve) = 1 - BR(A → p + e⁻ + ve) = 1 - (83 × 10⁻⁴) = 0.99917.
The measured value of the branching fraction of A → A⁺ + e⁺ + ve is BR(e+ve) = 2106 %.This is greater than 100%. Therefore, the value must be a typographical error. The correct percentage is probably 21.06%.The estimated branching fraction of A → A⁺ + e⁺ + ve is 99.917%, which is very close to 100%. This implies that the A mainly decays into A⁺ + e⁺ + ve.
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how can a hot water boiler heat water to 250°f and not boil the water
A hot water boiler uses a closed-loop system, where the water is circulated through pipes and heated by a burner or heating element.
The pressure in the system is controlled by a pressure relief valve, which prevents the water from boiling at normal operating temperatures. The boiling point of water increases as the pressure increases, so by keeping the pressure in the system above atmospheric pressure, the water can be heated to temperatures higher than its boiling point at standard pressure without boiling. This allows the hot water boiler to heat water to 250°F without boiling the water.
A hot water boiler can heat water to 250°F and not boil the water by using pressurization. When water is pressurized, its boiling point increases. In a sealed hot water boiler system, the pressure is increased, allowing the water to be heated beyond its normal boiling point of 212°F without turning into steam. This is possible due to the relationship between pressure and boiling point in a closed system, where increasing pressure raises the boiling point.
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1) Draw its Carnaugh map and Unit cube.
2) Find its minimal disjoctive normal form , using Carnaugh map or Unit cube
f(x, y, z)=(x + y)vz
These algebraic expressions should represent the function using the fewest possible number of literals. The final algebraic expression in the minimal disjunctive normal form is: (x'y'z) + (x'y'z') + (x'yz') + (x'yz)
The given expression is:f(x, y, z) = (x + y) v z1)
The Carnaugh map for this expression is: Unit Cube for the given expression:2) To find the minimal disjunctive normal form using the Carnaugh map or Unit cube, we need to: Identify the minterms that make up the function based on the Carnaugh map and the Unit cube.
Group the minterms together, ideally in groups of 2, 4, 8, or 16, such that each group covers all of the 1s in the Carnaugh map. Obtain an algebraic expression for each group of minterms. Combine the algebraic expressions obtained in the previous step. These algebraic expressions should represent the function using the fewest possible number of literals. These steps are shown below:
Minterms identified from the Carnaugh map: m1, m2, m5, m6.
Group the minterms such that each group covers all of the 1s in the Carnaugh map. The resulting groups are: m1 + m2 + m5 + m6. Obtain an algebraic expression for each group of minterms. The algebraic expression for this group of minterms is: (x'y'z) + (x'y'z') + (x'yz') + (x'yz)
Combine the algebraic expressions obtained in the previous step. These algebraic expressions should represent the function using the fewest possible number of literals. The final algebraic expression in the minimal disjunctive normal form is: (x'y'z) + (x'y'z') + (x'yz') + (x'yz)
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Baker Bill used 67 kilograms of flour on Monday. He used 48 kilograms of flour on Tuesday. How much did he use in all?
The total amount of flour he used in all is 115kg
What is Addition?One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.
Given that Baker Bill used 67 kilograms of flour on Monday. He used 48 kilograms of flour on Tuesday
We would add the kg of flour he used
This would be 67 + 48 = 115kg of flour
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Arches National Park is a desert landscape located in Utah. The park is filled with arches that have been formed by nature. The arches were once solid rock. Over time, extreme temperature changes and windy conditions have caused pieces of rock to crumble and blow away, leaving holes in the rock and forming the arches. Which of these processes is responsible for the formation of the arches?
a.cooling magma
b.weathering and erosion
c.compaction and cementation
d.increased geological pressures
The two properties that are
parts of refraction are ...
Answer:
-Relative refractive index– It is the ratio of speed of light in one medium to the speed of light in another medium
-Absolute refractive index– It is the ratio of light in vacuum to the speed of light in another medium.
Explanation:
The intensity of the distributed lood acting on the beams 25 kN/m.) Determine the magnitude of reaction at Express your answer to three significant figures and include the appropriate units O ? N Value Units Submit Request Answer Figure Part 6 1 of 1 Delane te zand y components of reaction all sing scalar notation Express your answers using three significant figures separated by a comma HV AED vec ?
The magnitude of reaction at the beam due to the distributed load of 25 kN/m is 625 N.
What is the magnitude of reaction to the distributed load?The magnitude of reaction at the beam can be determined by calculating the total force exerted by the distributed load. In this case, the distributed load is given as 25 kN/m. To find the magnitude of reaction, we multiply the distributed load by the length of the beam.
Therefore, the magnitude of reaction is 25 kN/m multiplied by the length of the beam in meters. By performing the calculation, we obtain the value of 625 N as the magnitude of reaction at the beam due to the distributed load. This represents the total force exerted by the distributed load on the beam.
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3,
V₁ =
I₁ =
R₁ = 2 [2]
VT= 34 [v]
IT =
RT
=
V₂ =
I₂ =
R₂ = 9 [2]
V3 =
I3 =
R3 = 3 [2]
=
First, we shall determine the equivalent of R₂ and R₃. Details below:
Resistor 2 (R₂) = 9 ΩResistor 3 (R₃) = 3 ΩEquivalent (R) = ?R = (R₂ × R₃) / (R₂ + R₃)
R = (9 × 3) / (9 + 3)
R = 2.25 Ω
Now, we shall determine the equivalent resistance, Rₜ for the circuit. Details below:
Resistor 1 (R₁) = 2 ΩEquivalent of R₂ and R₃ (R) = 2.25 ΩEquivalent resistance (Rₜ) = ?Rₜ = R₁ + R
Rₜ = 2 + 2.25
Equivalent resistance (Rₜ) = 4.25 Ω
How do i determine total current, Iₜ?The total current, Iₜ can be obtained as follow:
Equivalent resistance (Rₜ) = 4.25 ΩTotal voltage (Vₜ) = 34 VTotal current (Iₜ) = ?Current = Voltage / resistance
Iₜ = 34 / 4.25
Total current (Iₜ) = 8 A
How do i determine V₁, V₂, and V₃ ?Voltage in series connection are different.
V₁ is in series connection with the total voltage of V₂ and V₃. Thus, it's value can be obtained as follow:
Resistor 1 (R₁) = 2 ΩTotal current (Iₜ) = 8 AVotalge 1 (V₁) = ?V = IₜR₁
V₁ = 8 × 2
V₁ = 16 V
Voltage in parallel connection is the same through out the circuit.
Thus, V₂ and V₃ are in parallel connection. Thus we can obtain their value as follow:
Total current (Iₜ) = 8 AEquivalent of R₂ and R₃ (R) = 2.25 ΩVoltage V₂ = V₃ =?V₂ = V₃ = IₜR
V₂ = V₃ = 8 × 2.25
V₂ = V₃ = 18 V
How do i determine I₁?We can obtain I₁ as shown below:
Resistor 1 (R₁) = 2 ΩVoltage 1 (V₁) = 16 VCurrent 1 (I₁) = ?I₁ = V₁ / R₁
I₁ = 16 / 2
current 1 (I₁) = 8 A
How do i determine I₂?We can obtain I₂ as shown below:
Resistor 2 (R₂) = 9 ΩVoltage 2 (V₂) = 18 VCurrent 2 (I₂) = ?I₁ = V₂ / R₂
I₂ = 18 / 9
current 2 (I₂) = 2 A
How do i determine I₃?We can obtain I₃ as follow:
Resistor 3 (R₃) = 3 ΩVoltage 3 (I₃) = 18 VCurrent 3 (I₃) = ?I₃ = V₃ / R₃
I₃ = 18 / 3
current 3 (I₃) = 6 A
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Why is friction a problem in space travellers
What is mean by biodiversity???
Answer:
Biodiversity is the biological variety and variability of life on Earth. Biodiversity is a measure of variation at the genetic, species, and ecosystem level. Terrestrial biodiversity is usually greater near the equator, which is the result of the warm climate and high primary productivity.
Answer:
Bio means life
Explanation:
Biodiversity means life on earth.
A ball rolling down a hill was displaced 21.9 m while uniformly accelerating from rest. If the final velocity was 7.14 m/s, what was the rate of acceleration?
Answer:
a = 1.16 m/s²
Explanation:
In order to find the acceleration of the ball we will use 3rd equation of motion.
2as = Vf² - Vi²
where,
a = acceleration = ?
s = displacement = 21.9 m
Vf = Final Velocity = 7.14 m/s
Vi = Initial Velocity = 0 m/s (Since, ball starts from rest)
Therefore, using the values, we get:
2a(21.9 m) = (7.14 m/s)² - (0 m/s)²
a = (50.97 m²/s²)/(43.8 m)
a = 1.16 m/s²
Two straight parallel wires are separated by 6.9cm . There is a 2.4?A current flowing in the first wire.
Part A
If the magnetic field strength is found to be zero between the two wires at a distance of 2.9cm from the first wire, what is the magnitude of the current in the second wire?
Express your answer using two significant figures.
The magnitude of the current in the second wire is 2.4 A, if the magnetic field strength is found to be zero between the two wires at a distance of 2.9cm from the first wire.
When two parallel wires are present, and a current flows in one wire, then it produces a magnetic field around it. The magnetic field created by one wire affects the magnetic field produced by another wire. Due to the magnetic field interaction, a force is created between the wires. If the magnetic field strength between the wires is zero, then it means the magnetic fields of the wires cancel out.
Using Biot-Savart law, the magnetic field produced by the first wire is given by:
B₁ = μ₀I₁/2πd
where μ₀ is the magnetic constant, I₁ is the current in the first wire, and d is the distance between the two wires.
The direction of the magnetic field is perpendicular to the plane of the current and a circular path around the wire. If two parallel wires carry current in the same direction, they attract each other, and if the current is in the opposite direction, they repel each other.
As the magnetic field strength is zero between the wires at a distance of 2.9 cm from the first wire, the magnitude of the magnetic field produced by the second wire is given by:
B₂ = μ₀I₂/2πd
At the point where the magnetic field strength is zero, the sum of the two magnetic fields is zero.
Hence, we can write:
B₁ + B₂ = 0
μ₀I₁/2πd + μ₀I₂/2πd = 0
(μ₀/2πd) (I₁ + I₂) = 0
I₁ + I₂ = 0
I₂ = -I₁
I₂ = -2.4 A
I₂ has a magnitude of 2.4 A and is flowing in the opposite direction of the first wire.
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a) The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as: 30 = (0.02)+(0.06)w dt If the initial speed is zero and a step size of h = 0.
Using Runge-Kutta 2nd order Heun's method, the speed (w) at t = 0.8s is approximately 0.0081.
Given:
Voltage input (V) = 30V
Initial speed (w) = 0
Step size (h) = 0.4s
Time at which speed is to be determined (t) = 0.8s
We need to determine the speed (w) at t = 0.8s using Heun's method.
We have k₁ = f(t₁, W₁) = 0.02 + 0.06w₁ (using the given equation)
At t = 0 and w = 0 (initial conditions), we have:
k₁ = 0.02 + 0.06(0) = 0.02
We have k₂ = f(t₁ + h, w₁ + k₁h) = 0.02 + 0.06(w₁ + 0.02h)
So, at t = 0.4s and w = 0 (initial conditions), we have:
k₂ = 0.02 + 0.06(0.02 * 0.4) = 0.02 + 0.00048 = 0.02048
So, W₂ = w₁ + (k₁ + k₂)(h/2)
= 0 + (0.02 + 0.02048)(0.4/2)
= 0.04048(0.2)
= 0.008096
Therefore, using Runge-Kutta 2nd order Heun's method, the speed (w) at t = 0.8s is approximately 0.0081.
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The complete question is:
The speed of a motor supplied with a voltage input of 30V, assuming the system is without damping, can be expressed as 30 = (0.02)+(0.06)w dt If the initial speed is zero and a step size of h = 0.4 s, determine the speed w at t = 0.8 s by using the Runge-Kutta 2nd order Heun's method. Heun's method: Wi+1=W₁ = w₁ + (-/-^₁ + = -K ₂ ) h where, k₁ = f(t₁, W₁) and k₂ = f(t₁ + h, w₁ + k₁h), the speed (w) at t = 0.8s is approximately 0.0081.
Question 1: A man trailing a trolley bag and suddenly, the wheels of the trolley bag get locked. The man realises that he has to put extra effort to drag the bag. The man finds it difficult to drag the bag because
Answer: Because of the friction force acting directly on the bag.
Explanation:
The function of the wheels is diminish the effect of the friction force, when the friction pulls back, it makes the wheel rotate, and this force is not applied directly on the bag.
Now the wheels are not working, so now the friction is acting directly on the bag, this is why the mand finds more difficult to drag the bag.
PLEASE HELP ON EDGE I WILL GIVE U A BRAINLIST IF U GET IT RIGHT
When you create a best fit line what is the expected value of the slope?
When you create a best-fit line, the expected value of the slope represents the average rate of change in the dependent variable (y) for every unit increase in the independent variable (x). The slope helps you make predictions and understand the relationship between the two variables in your dataset.
When you create a best-fit line, the expected value of the slope is the coefficient that represents the rate of change between the two variables being analyzed. The slope is determined by finding the ratio of the change in the dependent variable to the change in the independent variable.
It is important to note that the slope of a best-fit line is not always a perfect representation of the true relationship between the variables, but rather an approximation based on the available data. Therefore, the expected value of the slope is subject to variation and uncertainty depending on the specific data set and methodology used to create the best-fit line.
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can nak ed eye detect ray of all type? why?
Answer:
no
Explanation:
but different animals can
Answer: No, our eyes only see visible light
Explanation:
The n*ked eye can only detect electromagnetic radiation in the wavelength between 400nm-700nm. This is just how our eyes work. On the E&M spectrum, this band of light which we can see is called "visible light" because its the only light we can visibly see. The others forms of radiation must be seen with the use of technology
Kenny wants to get to Washington DC within 4 hours. Washington DC is 133 miles away from where he is. What is the avg speed he must go in order to meet his time frame ?
The measurement of voltage requires to place the voltmeter leads across the component whose voltage you wish to determine True False
The given statement "The measurement of voltage requires to place the voltmeter leads across the component whose voltage you wish to determine" is true.
The voltage is the difference in electrical potential between two points in a circuit, or it's the amount of electrical potential energy in a circuit. Voltage is measured in volts using a voltmeter, which is a device that measures the potential difference between two points in a circuit. Voltage is generally referred to as electric potential energy per unit charge.
As we know, every electrical circuit has a voltage that is the difference between the circuit's potential energy and the potential energy of the circuit's surroundings. The voltage across a component in a circuit is determined by comparing the potential energy on each side of the component.
A voltmeter is a device used to calculate this voltage. It works by measuring the voltage difference between two points in a circuit.The voltmeter is connected in parallel with the component whose voltage is being measured. The two leads of the voltmeter are connected in parallel with the component.
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a horizontal spring has a spring constant k =1000 n/m . a block with mass m = 10 kg approaches the spring with speed v0 = 1 m/s find the maximum compression of the spring.
The maximum compression of the spring due to the block of mass 10kg is 3.16 m
The spring constant of a horizontal spring, k = 1000 n/m
The mass of the block which compresses the spring, m = 10kg
= 10000 g
The speed of the block, v = 1 m/s
We know that the kinetic energy of the block will be responsible for the compression of the horizontal spring.
Thus, the kinetic energy of the block = work done for compressing the horizontal spring
1/2 mv² = 1/2 kx²
where m is the mass of the block
v is the velocity of the block
k is the spring constant
x is the compression of the spring
Now, let us substitute the known values in the above equation, we get
1/2 (10000)(1)² = 1/2 (1000)(x)²
500x² = 5000
x² = 5000 / 500
x² = 10
x = √10
x = 3.16 m
Therefore, the maximum compression of the spring is 3.16m
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please help me guys never mind the calculations
The shape is connected in parallel so;
5.1) Ans;
\( \frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} \\ \frac{1}{R} = \frac{1}{2} + \frac{1}{3} \\ \frac{1}{R} = \frac{3 + 2}{6} = \frac{5}{6} \\ R = \frac{6}{5} = 1.2 \: \: ohm\)
5.2) Ans;
\( \frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} \\ \frac{1}{R} = \frac{1}{8} + \frac{1}{10} \\ \frac{1}{R} = \frac{5 + 4}{40} = \frac{9}{40} \\ R = \frac{40}{9} = 4.4 \: \: ohm\)
I hope I helped you^_^
is the force ratio fp/fe greater than 1, less than 1, or equal to 1? explain.
The force ratio fp/fe is equal to 1. This is because the unsigned charges of the proton and the electron are equal, and they experience the same electric field. The magnitude of the electric force experienced by a charged particle in an electric field at a position is equal to the product of the electric field and the unsigned charge of the particle.
F = qE
where
F is the force
q is the charge
E is the electric field
The proton and the electron have the same charge, so the magnitude of the force they experience is equal. The electric field is also the same, so the force ratio fp/fe is equal to 1.
fp/fe = q_p E / q_e E = 1
In other words, the force on the proton is equal to the force on the electron.
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Suppose a spring weh sping constant 3 N/m is horizonal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 0.8 Ha (Cycles pet second). What is the mass? Assume there is no friction
Mass = heip (units)
The mass of the object attached to the spring is approximately 0.119 kg.
To determine the mass of the attached object using the spring, we can utilize Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force exerted by the spring,
k is the spring constant, and
x is the displacement of the spring from its equilibrium position.
The frequency of the spring's motion (f) can be related to the mass (m) and the spring constant (k) using the equation:
f = (1 / (2π)) * √(k / m)
Rearranging this equation, we can solve for the mass:
m = (k / (4π² * f²))
Given:
Spring constant (k) = 3 N/m
Frequency (f) = 0.8 Hz
Substituting these values into the equation, we get:
m = (3 N/m) / (4π² * (0.8 Hz)²)
Calculating this expression:
m ≈ 0.119 kg
Therefore, the mass of the object attached to the spring is approximately 0.119 kg.
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The mass attached to the spring is approximately 0.238 kg.
To find the mass attached to the spring, we can use the formula for the angular frequency (ω) of a mass-spring system:
ω = √(k / m),
where ω is the angular frequency, k is the spring constant, and m is the mass.
Given:
k = 3 N/m (spring constant),
f = 0.8 Hz (frequency).
First, let's convert the frequency from Hz to radians per second (rad/s):
ω = 2πf = 2π(0.8) ≈ 5.03 rad/s.
Now, we can solve the formula for m:
ω = √(k / m),
m = k / ω^2,
m = 3 N/m / (5.03 rad/s)^2.
Calculating the value:
m ≈ 3 N/m / (5.03 rad/s)^2 ≈ 0.238 kg.
Therefore, the mass attached to the spring is approximately 0.238 kg.
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in gel electrophoresis, dna fragments migrate toward the negative pole of the electric field. t/f
The given statement is true.
In gel electrophoresis, an electric field is applied to a gel matrix containing charged molecules such as DNA fragments. The electric field exerts a force on the charged molecules, causing them to migrate through the gel matrix.The DNA fragments are negatively charged due to the phosphate groups in their structure, and as a result, they migrate toward the positive pole of the electric field. However, since the gel electrophoresis apparatus is designed such that the negative electrode (cathode) is placed at the bottom of the gel, and the positive electrode (anode) is placed at the top, the DNA fragments move toward the negative pole. This is because the negatively charged molecules are attracted to the positively charged anode at the top of the gel, and move away from the negatively charged cathode at the bottom.To know more about electric field visit:
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An object launched at 65 degrees from the horizontal would have the same range
(distance travelled) as an object launched from? Write only the WHOLE number with
no units (example: 65)
Answer:
An object launched from 65° will have the same range as an object launched from 25°
Explanation:
The formula for the horizontal range, R, is given as follows;
\(R = \dfrac{v \times sin(2\cdot \theta)}{g}\)
Therefore, given that sinθ increases from 0 to 1 for θ values from 0 to 90° and decreases from 1 to 0 for θ values from 90° to 180°, and that the values of sin(θ) are positive in the first and second quadrant, we have that for the given angle, θ = 65°, the range is therefore;
\(R = \dfrac{v \times sin(2\times 65 ^{\circ})}{g} = \dfrac{v \times sin(130 ^{\circ})}{g}\)
The location of 130° = Second quadrant
A rotation of 130° in the counterclockwise is equivalent to a rotation of 50° in the clockwise direction
Therefore, we have sin(130°) = sin(50°)
Therefore, the range for 130°/2 = 65° is the same as the range for 50°/2 = 25° and an object launched from 65° will have the same range as an object launched from 25°.