The minimum work needed to pus the cart up the inclined plane is 960000 J.
What is work done on a inclined plane?The work done on a inclined plane is given below as:
Work done = force * distanceDistance = 700 m
The force on an inclined plane, F = mgsinθ
where;
m is mass in kg
g = 9.81 m/s²
θ = 8.5°
Work done = 950 * 9.81 * sin 8.5 * 700
Work done = 960000 J
Therefore, minimum work needed is 960000 J.
In conclusion, the work done is a product of force and distance.
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How does the human system of reproduction result in people getting one copy of a sickle cell gene and one copy of a normal gene? Describe the process
The sickle cell gene must be inherited from both parents for a kid to be born with sickle cell disease.
Haemoglobin synthesis in red blood cells is controlled by the genes linked to sickle cell disease.
Two typical genes are present in most persons for haemoglobin. Certain individuals have one gene for normal haemoglobin and one for sickle haemoglobin. Sickle cell trait refers to this.
In nearly every way, these people are normal. People who have sickle cell trait never develop into sickle cell disease.
Rarely did people with sickle cell trait have issues linked to their single sickle cell gene, and even then, only in rare cases.
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I love you
Please answer my question :-)
Answer:
A- Astronomical body
C- Galaxy
D- Comet
B- Moon
Hope this helps you! Have a great day!
Answer:
1. A
2. C
3. D
4. B
Explanation:
30 A student blows air through a liquid using a straw. This causes the liquid to evaporate quickly and therefore to cool. Which statement explains why the remaining liquid cools?
A Slower-moving molecules are carried away by the air bubbles. B The air molecules conduct heat from the liquid. C The air sets up convection currents in the liquid. D The molecules with most energy leave the liquid.
The correct statement is B that explains why the remaining liquid cools when a pupil blows air through it using a straw .
The air molecules conduct heat from the liquid. When air is blown through a liquid, the moving air motes come into contact with the liquid motes and transfer some of their kinetic energy to them.
This transfer of energy results in the liquid motes gaining kinetic energy, which in turn causes the liquid to dematerialize snappily, leading to cooling.
Also, the air molecules also carry away some of the heat from the liquid's face, performing in farther cooling. This process is called convection and involves the movement of liquid due to the temperature differences created by the blown air.
Thus, Option B, which states that the air motes conduct heat from the liquid, is the most accurate explanation for why the remaining liquid cools.
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can you ans please ?????????????????????????????????????????
Answer:
ans a
Explanation:
as the circuit should not be completed until switch is closed
Centripetal force
A. causes objects to increase their speed.
B. does not affect the speed of object.
C. does not change the velocity of an
object.
D. causes objects to slow down.
Answer:
C. does not change the velocity of an object.
Explanation:
Centripetal force is the force that acts on an object moving in a circular path and is directed towards the center of the circle. It is responsible for changing the direction of the object's velocity towards the center of the circle, but it does not change the magnitude of the velocity, which means that it does not affect the speed of the object. Therefore, option B and D are incorrect. The direction of the velocity is constantly changing due to the centripetal force, but the magnitude of the velocity, or speed, remains constant. Option A is also incorrect because centripetal force is not responsible for increasing the speed of the object, but rather for changing the direction of its velocity.
A flat-bottomed barge loaded with coal has a mass of 4.80 × 105 kg. The barge is 20.0 m long and 10.0 m wide. It floats in fresh water. What is the depth of the barge below the waterline?
The depth of the barge below the waterline is 2.40 m.
To calculate the depth of the barge below the waterline, we need to consider the buoyancy force acting on the barge. The buoyancy force is equal to the weight of the water displaced by the barge.
First, we need to calculate the volume of water displaced by the barge.
Since the barge is flat-bottomed, we can assume that the shape of the displaced water is rectangular with a length of 20.0 m, a width of 10.0 m, and a depth of d (which is what we're trying to find).
Therefore, the volume of water displaced is V = 20.0 m x 10.0 m x d = 200.0 m³.
The weight of the displaced water can be calculated using its density and volume. In fresh water, the density of water is approximately 1000 kg/m³.
Therefore, the weight of the displaced water is W = 1000 kg/m³ x 200.0 m³ = 2.00 × 10⁵ kg.
Since the buoyancy force is equal to the weight of the displaced water, we have [tex]F_b[/tex] = W = 2.00 × 10⁵ kg.
The weight of the barge is [tex]W_b[/tex] = 4.80 × 10⁵ kg. According to Archimedes' principle, the buoyancy force acting on an object in a fluid is equal to the weight of the fluid displaced by the object, so we can write:
[tex]F_b[/tex] = [tex]W_b[/tex] - [tex]W_d[/tex]
where [tex]W_d[/tex] is the weight of the water displaced by the submerged part of the barge. Solving for [tex]W_d[/tex], we get:
[tex]W_d[/tex] = [tex]W_b[/tex] - [tex]F_b[/tex] = 4.80 × 10⁵ kg - 2.00 × 10⁵ kg = 2.80 × 10⁵ kg.
The volume of water displaced by the submerged part of the barge is equal to the volume of the rectangular prism with a length of 20.0 m, a width of 10.0 m, and a depth of d. Therefore, we can write:
[tex]V_d[/tex] = 20.0 m x 10.0 m x d = 200.0 m³ x (d/10.0)
The weight of the displaced water is also equal to its density times its volume, so we have:
[tex]W_d[/tex] = 1000 kg/m³ x [tex]V_d[/tex]
Substituting [tex]V_d[/tex] in terms of d and solving for d, we get:
d = ([tex]W_d[/tex] / (1000 kg/m³ x 200.0 m²)) x 10.0 m = (2.80 × 10⁵ kg / (1000 kg/m³ x 200.0 m²)) x 10.0 m = 2.40 m
Therefore, the depth of the barge below the waterline is 2.40 m.
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during SHM an object has_____________at mean position
(a)P.E=0,K.E=0
(b)P.E=K.E
(c)P.E=MAX,K.E=0
(d)P.E=0,K.E=MAX
During Simple Harmonic Motion (SHM), an object at the mean position has potential energy (P.E)=0 and kinetic energy (K.E)=MAX. So, the correct option is (d).
In Simple Harmonic Motion (SHM), an object oscillates about a mean position, with the motion characterized by a restoring force proportional to its displacement from the mean position.
When the object is at the mean position, it has maximum kinetic energy (K.E) because it is at its maximum velocity, and it has zero potential energy (P.E) since it is not displaced from the equilibrium position.
As the object moves further from the mean position, its P.E increases, and K.E decreases. The correct answer to the question is option (d), where P.E=0 and K.E=MAX at the mean position.
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Which of the following helps prevent and cope with heat-related conditions?
Drinking water
Wear proper clothing
Rest frequently
all of the above
An action which would help in preventing and coping with heat-related conditions is: A. Drinking water.
What is heat?Heat can be defined as a form of energy that is transferred from a physical object (body) to another, as a result of a difference in temperature. Also, heat is a condition of weather that is generally characterized by a high degree of temperature.
This ultimately implies that, heat is most likely to cause dehydration and high body temperature.
In order to prevent and cope with heat-related conditions, you should ensure that you drink water at regular intervals for hydration.
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The blood pressure at your heart is approximately 100 mm Hg. As blood is pumped from the left ventricle of your heart, it flows through the aorta, a single large vessel with a diameter of about 2.5 cm. The speed of blood flow in the aorta is about 60 cm/s. Any change in pressure as blood flows in the aorta is due to the change in height: the vessel is large enough that viscous drag is not a major factor into successively smaller and smaller blood vessels until it reaches the capillaries. Blood flows in the capillaries at the much lower speed of approximately 0.7 mm/s. The diameter of capillaries and other small blood vessels is so small that viscous drag is a major factor..Because the flow speed in your capillaries is much less than in the aorta, the total cross-section area of the capillaries considered together must be much larger than that of the aorta. Given the flow speeds noted, the total area of the capillaries considered together is equivalent to the cross-section area of a single vessel of approximately what diameter?
a. 25 cm
b. 50 cm
c. 75 cm
d. 100 cm
Answer:
The correct option is c. 75 for this question
Explanation:
The correct option is c. 75 for this question:
Let's see how.
Continuity Equation is given as:
AcVc = AaVa
Where,
Aa = Area of Aorta
Ac = Area of the capillary
Va = Fluid speed in Aorta
Vc = Fluid speed in Capillary
So,
Assuming the fluid is the ideal one/
[tex]\pi[/tex]/4 [tex]Dc^{2}[/tex] Vc= [tex]\pi[/tex]/4 [tex]Da^{2}[/tex] Va
[tex]Dc^{2}[/tex] Vc= [tex]Da^{2}[/tex] Va
Dc = Da x [tex]\sqrt{\frac{Va}{Vc} }[/tex]
Dc = 2.5 cm x [tex]\sqrt{\frac{60 cm}{0.07 cm } }[/tex]
Dc = 73.192 cm
Dc = 75 approximately
Hence, the diameter of the capillary = 75 cm approximately
BEST ANSWER = BRAINLIEST
An object with a charge of +1 C is 10 mm from an object with a charge of +1 C. Based on the data in the table, which type and amount of electrical force will there most likely be between the two objects? Explain your answer
Answer: Weak or repulsive
Explanation: The amount of electrical force would be weak based on the distance between the two objects.
Based on the data in the table, the two objects will have a repulsive force of medium strength.
How to find type and amount?This is because the two objects have the same charge, and like charges repel each other. The force is calculated using the following formula:
F = k × (Q₁ × Q₂) / r²
where:
F = force in newtons
k = Coulomb's constant (8.988 x 10⁹ N m²/C²)
Q₁ and Q₂ = charges in coulombs
r = distance between the charges in meters
In this case:
F = medium
k = 8.988 x 10⁹ N m²/C²
Q1 = Q2 = +1 C
r = 10 mm = 0.01 m
Substituting these values into the formula gives:
F = (8.988 x 10⁹ N m²/C²) × (+1 C × +1 C) / (0.01 m)²
= 8.988 x 10⁶ N
Therefore, the two objects will have a repulsive force of medium strength.
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The "seeing" ability, or resolution, of radiation is determined by its wave length
The mass of an electrons is 9.10939 * 10^-31 kg and Planck's constant is 6.62607 * 10^-34 Js
If the size of an atom is an the order of 0.08 nm, how fast must an electron travel to have a wavelength small enough to "see" an atom? Answer in the units of m/s
You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done?
Our intrepid hero has done 2,332,000 joules of work pushing the crate on the frictionless surface of the new planet.
To compute the work done by the space wayfarer, we want to involve the recipe for work, which is work = force x distance. For this situation, the power can be determined utilizing the recipe force = mass x speed increase, which gives us force = 220 kg x 2 m/s^2 = 440 N.
The distance moved by the traveler is given as 5.3 km, however we want to change this over completely to meters by duplicating by 1000, which gives 5300 m.
Accordingly, the work done by the wayfarer is work = 440 N x 5300 m = 2,332,000 J.
Thus, our fearless legend has completed 2,332,000 joules of work pushing the container on the frictionless surface of the new planet.
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A transformer used on a 220V line deliver 1.5A at 1800V. what current is drawn from the line assuming the ideal Transformers
The current drawn from the line, assuming an ideal transformer, is approximately 12.27A.
In an ideal transformer, the power remains the same before and after transformation. Therefore, we can use the power equation to determine the current drawn from the line.
The power equation for a transformer is given by:
P1 = P2
where P1 is the input power, P2 is the output power.
Given that the input voltage (V1) is 220V, the input current (I1) is unknown, the output voltage (V2) is 1800V, and the output current (I2) is 1.5A, we can rewrite the equation as:
V1 * I1 = V2 * I2
Substituting the known values:
220V * I1 = 1800V * 1.5A
Simplifying:
I1 = (1800V * 1.5A) / 220V
I1 ≈ 12.27A
Therefore, the current drawn from the line, assuming an ideal transformer, is approximately 12.27A.
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Which of the following gases is the major byproduct of fossil fuel combustion?
methane
water vapor
sulfuric acid
carbon dioxide
Answer:
Carbon dioxide and water vapour
Explanation:
So the products of a combustion reaction are primarily:
carbon dioxide + water vapour, however other gases such as nitrogen, methane, and sulphur dioxide are also produced in smaller concentrations.
Carbon dioxide and water vapour are the main byproducts
Answer:
Carbon dioxide
Explanation:
The major byproduct of fossil fuel combustion is carbon dioxide. When fossil fuels such as coal, oil, and natural gas are burned, they release carbon dioxide into the atmosphere. This is because fossil fuels are made up of hydrocarbons, which are compounds made up of carbon and hydrogen. When these compounds are burned, they react with oxygen in the air to produce carbon dioxide [tex]\rm (CO_2)[/tex] and water vapor [tex]\rm (H_2O)[/tex].
Methane is also produced during fossil fuel combustion, but in smaller amounts compared to carbon dioxide. Sulfuric acid is not a byproduct of fossil fuel combustion, but rather a product of the reaction between sulfur dioxide [tex]\rm (SO_2)[/tex] and water vapor in the atmosphere. While water vapor is also produced during fossil fuel combustion, it is not considered a major byproduct, as it is a natural component of the air and atmosphere.
A seesaw is balanced on a pivot point. If a 20 kg child sits 1 meter from the pivot point, how far from the pivot point should a 40 kg child sit in order to balance the seesaw?
Okay, here are the steps to solve this problem:
1) The seesaw is balanced when the sum of moments is 0.
2) The moment created by a force depends on the force and the perpendicular distance from the pivot point.
3) The 20 kg child sits 1 meter from the pivot. So its moment is 20 * 1 = 20 kg*m.
4) We want to find the distance for the 40 kg child to create a moment that balances the 20 kg child's moment.
5) So the moment of the 40 kg child must be 20 kg*m.
6) The moment depends on force and distance. We know the force is 40 kg.
7) So we set: 40 kg * distance = 20 kg*m
8) And solve for the distance: distance = 20 / 40 = 0.5 meters
Therefore, for the seesaw to balance with a 20 kg child 1 meter from the pivot and a 40 kg child on the other side, the 40 kg child should sit 0.5 meters from the pivot point.
Let me know if you have any other questions!
In which circuit would ammeter A shows the greatest current?
In the circuit with two 10Ω resistors in parallel, ammeter A would show the greatest current. This is because, in a parallel circuit, the total resistance is lower than in a series circuit, which means that the current can flow more easily.
In this case, the two 10Ω resistors in parallel create a total resistance of 5Ω (1/Rtotal = 1/10 + 1/10 = 2/10, Rtotal = 10/2 = 5), while in the series circuit,https://brainly.com/question/11409042?referrer=searchResults the total resistance would be 20Ω (10 + 10). Ohm's law states that the current is directly proportional to the voltage and inversely proportional to the resistance, so the circuit with lower resistance will allow for greater current flow.
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--The complete Question is, In which circuit would ammeter A show the greatest current: a circuit with one 6V battery and two 10Ω resistors in parallel or a circuit with one 6V battery and two 10Ω resistors in series? --
You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done?
Our intrepid hero has done 2332 kJ of work pushing the crate on the frictionless surface of the newly discovered planet.
The work done by the space traveler can be determined utilizing the recipe W = F x d, where W is work, F is power, and d is distance. To find the power, we can utilize the recipe F = m x a, where m is mass and an is speed increase. Connecting the given qualities, we get F = 220 kg x 2 m/s^2 = 440 N.
Presently we can compute the work done by increasing the power by the distance: W = 440 N x 5.3 km = 2332 kJ. Accordingly, our fearless legend has done 2332 kJ of work pushing the container on the frictionless surface of the newfound planet.
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a girl whose mass is 40kg walk up a flight of 20steps each 15mm hight in 10seconds.find power developed by the girl showing the solution
Answer: Approximately 11.76 joules per second
=========================================================
Work Shown:
Mass = 40 kg
Force pulling down = (mass)*(gravity) = 40*9.8 = 392 newtons
Roughly 392 newtons of force are pulling down on her.
To climb the steps, she must apply 392 newtons of force upward.
---------------
Displacement = 20*(15 mm) = 300 mm = 0.3 m
Work = Force*Displacement
Work = 392*0.3
Work = 117.6 joules of energy
---------------
Power = (Work)/(Time)
Power = (117.6 joules)/(10 seconds)
Power = (117.6/10) joules per second
Power = 11.76 joules per second, which is approximate
What information do you need to collect in order to study an object’s motion?
The information we will need to demonstrate that an object is in motion include;
initial position of the objectfinal position of the objecttime difference between the initial and final position of the objectWhat is an object in motion?An object is in motion when it changes its position with time, relative to a stationary object.
Mathematically, we can use the following equation to demonstrate the motion of an object.
v = Δx / Δt
where;
Δx is the change in the position of the objectΔt is the change in time of motion of the objectSo the data we will need to demonstrate that an object is in motion include;
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How does altitude from the surface of earth affect the time period of a simple pendulum
Answer:
because the strength of Earth's gravitational field is not uniform everywhere, a given pendulum swings faster, and thus has a shorter period, at low altitudes and at Earth's poles than it does at high altitudes and at the Equator.
A motorcyclist is making an electric vest that, when connected to the motorcycle's 12 V battery, will warm her on cold rides. She is using 0.25-mm-diameter copper wire, and she wants a current of 4.2 A in the wire. Part A What length wire must she use
Answer:
L = 8.35 m
Explanation:
The lenght of a wire L can be calculated using the following expression:
L = R A/ρ (1)
Where:
R: resistance of the wire
A: Cross section area of the wire
ρ: resistivity of the copper wire.
With this expression we realize that we do not have the area of the cross section, and the resistance of the wire either.
To calculate the area we can use the following expression:
A = πr² (2)
If the diameter is 0.25 mm, then the radius is half, 0.125 mm. Converting this in meter it will have to be:
0.125 /1000 = 0.000125 m
Replacing we have:
A = π(0.000125)²
A = 4.91x10⁻⁸ m²
The reported resistivity of a copper wire is 1.68x10⁻⁸ Ω.m, so we just need to determine the resistance, which can be found using Ohm's law:
R = V/I (3)
Replacing (3) into (1) we have:
L = (V * A) / (I * ρ) (4)
So finally, the length of the copper wire will be:
L = (12 * 4.91x10⁻⁸) / (4.2 * 1.68x10⁻⁸)
L = 8.35 mHope this helps
an answer With a velocity of 45 ms comes in to land at the start of the runway and brakes a far will it travel before coming to a stop if the runway is 275 m long? (3 marks) wit it take to shot? (3 marks)
With a velocity of 45 m/s comes in to land at the start of the runway and brakes. The distance the plane will travel before coming to a stop is approximately 22.5a meters if the runway is 275 m long.
To determine how far the plane will travel before coming to a stop, we can use the equations of motion.
Let's assume the initial velocity of the plane is 45 m/s, the distance it travels before coming to a stop is 'd', and the length of the runway is 275 m.
Using the equation of motion:
v² = u² + 2as
where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration, and 's' is the distance traveled.
Since the plane comes to a stop, the final velocity 'v' is 0 m/s.
Therefore, the equation becomes:
0 = 45² + 2a * d
Rearranging the equation, we get:
2a * d = -45²
d = (-45²) / (2a)
To find the value of 'a', we can use the equation:
a = (v - u) / t
where 't' is the time taken to stop.
Since the final velocity is 0 m/s and the initial velocity is 45 m/s, the equation becomes:
0 = (0 - 45) / t
Solving for 't', we find:
t = 45 / a
Now, substituting the value of 'a' into the equation for 'd', we get:
d = (-45²) / (2 * (45 / a))
Simplifying the expression, we have:
d = (-45² * a) / (2 * 45)
d = -45a / 2
d = -22.5a
Since the acceleration 'a' is negative (opposite direction to the initial velocity), the distance 'd' will also be negative. However, we are only interested in the magnitude of the distance traveled.
As for the time it takes to stop, we can use the equation t = 45 / a, where 'a' is the acceleration. The time taken to stop will be the same as the time taken to decelerate from the initial velocity of 45 m/s to 0 m/s.
In summary, the plane will travel approximately 22.5 times the acceleration distance before coming to a stop, and the time it takes to stop will be 45 divided by the acceleration.
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Pls solve 50 points!!!!!!!!!
Refer to the attachment for solution
A steel cylinder of length 10 cm, mass 160 g and density 8 g/em. The radius of the cylinder is
Answer:
0.8cm
Explanation:
Volume = mass/density = 160/8 = 20cm³
Volume = πr²h
r² = v/πh = 20/10π =0.64
r = √0.64 = 0.8
Work is a measurement of the transfer of which of the following?
A. Impulse
B. Power
C. Energy
Answer:Enegry
Explanation:Energy transfer is used to do work
The low-frequency speaker of a stereo set has a surface area of and produces 1W of acoustical power. What is the intensity at the speaker
Answer:
I = [tex]\frac{1}{4\pi \ r^2}[/tex]
we see the intensity decreases with the inverse of the distance squared
Explanation:
Intensity is defined as power per unit area,
I = P / A
in this case we have that the sound is emitted in a spherical form therefore the area is
A = 4 pi r2
therefore the intensity is
I = [tex]\frac{1}{4\pi \ r^2}[/tex]
as we see the intensity decreases with the inverse of the distance squared
What is the equivalent resistance of this network?
The equivalent resistance of the circuit network is determined as 1.6 ohms.
What is the equivalent resistance of the network?The equivalent resistance of the circuit network is calculated as follows;
To determine the equivalent resistance of the circuit, we will decompose the circuit into series and parallel components.
The equivalent resistance at J₄ is calculated as follows;
The two 4 ohms are in series;
J₄ = 4Ω + 4 Ω = 8 Ω
The equivalent resistance at J₁ is calculated as follows;
The 4 ohms and 0 ohm are in series;
J₁ = 0 Ω + 4 Ω = 4 Ω
The equivalent resistance at J₂ and J₃ is calculated by applying the formula for parallel resistors;
1/Re = 1/J₁ + 1/J₄ + 1/J₂,₃
1/Re = 1/4 + 1/8 + 1/4
1/Re = 5/8
Re = 8/5
Re = 1.6 ohms
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how is work and energy inter-related?? (in simple words)
Answer:
The work and energy is inter- related because if we are energetic then only we are able to work.
People who are weak and not energetic cannot work continuously.
Explanation:
hope this helps you....
f body with a mass of 6kg. (Ans: When we throw a stone with 12 N force to produce an acceleration of m/s², what is the mass of 6 kg? (Ans: 1.5kg) Calculate the acceleration produced when a force of 48 N is What They m
a. When the force = 12 N, mass = 6 kg, the acceleration is a = 2 m/s²
b. When the force = 48 N, mass = 6 kg, the acceleration is a = 8 m/s².
What is the acceleration of the body?The acceleration of the body is calculated by applying Newton's second law of motion as follows;
F = ma
where;
F is the force applied to the objectm is the mass of the objecta is the acceleration of the objecta = F / m
when the force = 12 N, mass = 6 kg, the acceleration is calculated as;
a = 12 N / 6 kg
a = 2 m/s²
when the force = 48 N, mass = 6 kg, the acceleration is calculated as;
a = 48 N / 6 kg
a = 8 m/s²
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HELP PLEASE SolVE THANK SO MUCH
A mortar, angled 45 degrees from the horizontal, shoots a round with an initial velocity of 90 meters per second.
1) Draw a diagram of the described scenario and organize your
variables along x and y dimensions.
2) For when the round reaches maximum height, calculate for:
a) Time of travel
b) Horizontal displacement
3) For when the round reaches maximum range, calculate for:
a) Time of travel
b) Horizontal displacement
1. Diagram and Variables:
Maximum Height
|
|
|
|
|
|
|
|
|
------------------------ Ground ------------------------>
Variables:
Initial velocity (v₀) = 90 m/s
Launch angle (θ) = 45°
Maximum height (H)
Time of travel at maximum height (t_max_height)
Horizontal displacement at maximum height (d_max_height)
Time of travel at maximum range (t_max_range)
Horizontal displacement at maximum range (d_max_range)
2. For when the round reaches maximum height:
a) Time of travel (t_max_height):
At the maximum height, the vertical velocity (v_y) becomes zero. To find the time it takes for the round to reach the maximum height, we can use the equation for vertical motion:
v_y = v₀ * sin(θ) - g * t
0 = v₀ * sin(θ) - g * t_max_height
Solving for t_max_height:
t_max_height = v₀ * sin(θ) / g
Substituting the values:
t_max_height = 90 m/s * sin(45°) / 9.8 m/s²
Calculating the value:
t_max_height ≈ 6.12 s
b) Horizontal displacement (d_max_height):
The horizontal displacement at maximum height can be calculated using the equation:
d_max_height = v₀ * cos(θ) * t_max_height
Substituting the values:
d_max_height = 90 m/s * cos(45°) * 6.12 s
Calculating the value:
d_max_height ≈ 385.94 m
Therefore, at the maximum height, the time of travel is approximately 6.12 seconds, and the horizontal displacement is approximately 385.94 meters.
3. For when the round reaches maximum range:
a) Time of travel (t_max_range):
To find the time it takes for the round to reach the maximum range, we can consider the symmetry of projectile motion. The time of flight (t_flight) is twice the time it takes to reach maximum height:
t_flight = 2 * t_max_height
Substituting the value of t_max_height:
t_max_range = 2 * 6.12 s
Calculating the value:
t_max_range ≈ 12.24 s
b) Horizontal displacement (d_max_range):
The horizontal displacement at maximum range can be calculated using the equation:
d_max_range = v₀ * cos(θ) * t_max_range
Substituting the values:
d_max_range = 90 m/s * cos(45°) * 12.24 s
Calculating the value:
d_max_range ≈ 868.63 m
Therefore, at the maximum range, the time of travel is approximately 12.24 seconds, and the horizontal displacement is approximately 868.63 meters.
When a mortar is fired at an angle of 45 degrees, it will reach its maximum height in 6.49 seconds and its maximum range in 12.98 seconds. The horizontal displacement of the mortar when it reaches its maximum height will be 413.02 meters, and its horizontal displacement when it reaches its maximum range will be 826.53 meters.
1. To draw a diagram of the described scenario, you can start by drawing a coordinate system. The x-axis represents the horizontal direction, and the y-axis represents the vertical direction. Place the origin (0, 0) at the point of launch. Since the mortar is angled 45 degrees from the horizontal, you can draw a line representing the initial direction of the round at a 45-degree angle from the x-axis.
Next, label the variables along the x and y dimensions. For the x-dimension, you can label the variable as "horizontal displacement" or simply "x." For the y-dimension, you can label the variable as "vertical displacement" or "height" and indicate that it is measured in meters.
2. When the round reaches maximum height:
a)
The time of ascent can be calculated using the following formula:
time = ( initial velocity * sin(angle)) / acceleration due to gravity
In this case, the initial velocity is 90 meters per second, and the angle is 45 degrees. The acceleration due to gravity is typically considered to be approximately 9.8 meters per second squared.
Plugging in the values:
time = (90 * sin(45)) / 9.8 = 6.49s
b) The horizontal displacement at maximum height is :
horizontal displacement = initial velocity * cos (45) * time of ascent
Plugging in the values:
horizontal displacement=90* cos (45) * 6.49s= 413.02m
3. When the round reaches maximum range:
a) The time of travel can be calculated using the following formula:
time = (2 * initial velocity * sin(angle)) / acceleration due to gravity
The initial velocity and angle remain the same.
Plugging in the values:
time = (2 * 90 * sin(45)) / 9.8= 12.98s
b) The horizontal displacement at maximum range can be calculated using the following formula:
horizontal displacement = (initial velocity^2 * sin(2*angle)) / acceleration due to gravity
Plugging in the values:
horizontal displacement = (90^2 * sin(2*45)) / 9.8= 826.53m
Therefore, A mortar will reach its maximum height and distance when shot at a 45-degree angle in 6.49 and 12.98 seconds, respectively. When the mortar achieves its maximum height, its horizontal displacement will be 413.02 meters, and when it reaches its maximum range, it will be 826.53 meters.
To learn more about projectile motion click:
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