Answer:
-2 m/s and the average acceleration is 2 m/s².
Explanation:
To find the average velocity of particle P over the time interval 1<=t<=3 sec, we need to use the following formula:
average velocity = (final displacement - initial displacement) / (final time - initial time)
In this case, the initial time is 1 sec and the final time is 3 sec. Therefore, the initial displacement is:
x(1) = 1² - 6(1) = -5
And, the final displacement is:
x(3) = 3² - 6(3) = -9
Now, we can substitute the values in the formula:
average velocity = (-9 - (-5)) / (3 - 1) = -2 m/s
To find the average acceleration of particle P over the time interval, we need to use the following formula:
average acceleration = (final velocity - initial velocity) / (final time - initial time)
We know that the initial time is 1 sec, the final time is 3 sec, and the initial velocity is the velocity at time t=1 sec. Therefore, the initial velocity is:
v(1) = 2t - 6 = 2(1) - 6 = -4 m/s
We also know that the final velocity is the velocity at time t=3 sec. Therefore, the final velocity is:
v(3) = 2t - 6 = 2(3) - 6 = 0 m/s
Now, we can substitute the values in the formula:
average acceleration = (0 - (-4)) / (3 - 1) = 2 m/s²
Therefore, the average velocity of particle P over the time interval 1<=t<=3 sec is -2 m/s and the average acceleration is 2 m/s².
A 2.1 x 103 kg car starts from rest in a driveway. An average force of 4.0 x 103 N act on the car so that the car’s speed at the end of the driveway is 3.8 m/s. What was the length of the driveway?
Answer:
Explanation:
We can use the kinematic equation v^2 = u^2 + 2as to solve for the length of the driveway. Here, u = 0 (since the car starts from rest), v = 3.8 m/s, a = F/m = 4.0 x 10^3 N / 2.1 x 10^3 kg = 1.9 m/s^2. Solving for s, we get:
s = (v^2 - u^2) / 2a = (3.8^2) / (2 x 1.9) = 3.8 m
So the length of the driveway is 3.8 meters.
What is the electric potential energy of the group of charges in the figure? (Figure 1)
that the relative placements of the charges as well as their multiples affect a set of ions' potential energy. When the specific charge have the same sign or have equal signs, the energy is positive. Or else, it is negative.
How is potential energy calculated?The force acting just on two objects affects the potential energy formula. The formula for gravitational force is P.E. (= mgh, where g seems to be the acceleration caused by gravity (9.8 m/s2 at the earth's surface) while h represents the elevation in metres.
What is a system with two charges' potential energy?As a result, the system's potential energy equals the sum of a work that was done to set up the entire system of two counts. The potential energy that exists in the combination of two charges in such an external field can be stated as follows: q1V(r1) = q2V(r2) + (q1q2/4or12).
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A power plant involves thermodynamic cycles to generate electrical power. In the first stage, water is pumped under saturated conditions from a pressure of 0.7 bar to 30 bar. Water then goes to the boiler at constant pressure and leaves the boiler at 500°C. In this condition, the steam is then expanded isentropically in a steam turbine so that the pressure returns to 0.7 bar and is cooled in a condenser. Determine:
a) Pump work
b) The incoming heat is given to the boiler
c) Turbine work
d) The heat removed by the condenser
e) Cycle thermal efficiency
Two hot air balloons with the same mass and amount of helium put inside of them if one is a rigid material and the other expands which one would be the highest?
Answer:
One is that atmospheric pressure is dramatically reduced at high altitudes, so a helium balloon expands as it rises and eventually explodes. If you inflate a balloon beyond its limits at room temperature, it will break into small pieces up to about ten centimetres long
Explanation:
Which material would you choose to make the handrails of the playhouse? Use the data to explain your reasoning.
Answer:
Explanation:
To choose a material for the handrails of the playhouse, we need to consider its strength and durability. One option could be stainless steel, which has a high tensile strength and is resistant to corrosion and weathering. Another option could be treated wood, which is also strong and can be treated to resist moisture and insects. Ultimately, the choice would depend on factors such as cost, aesthetics, and availability of materials.
A student uses 800 W microwave for 30 seconds how much energy does a student use
Answer:
The student used 24000 Joules of energy.
Explanation:
We can use the Energy Power equation to solve this example.
[tex]\sf E=Pt[/tex]
Where
[tex]\sf E[/tex] is the energy in Joules (J)
[tex]\sf P[/tex] is the power in Watts (W)
[tex]\sf t[/tex] is the time in seconds (s)
Numerical Evaluation
In this example we are given
[tex]\sf P=800\\t=30[/tex]
Substituting our given values into the equation yields
[tex]\sf E=800 \cdot 30[/tex]
[tex]\sf E=24000[/tex]
24000 Joules
[tex]\Large\bold{SOLUTION}[/tex]
To calculate the energy used by the student in this scenario, we can use the formula:
[tex]\sf{Energy\: (in\: Joules) = Power\: (in\: Watts) \times Time\: (in\: seconds)}[/tex]
Given that the student uses an 800 W microwave for 30 seconds, we can plug in these values to the formula:
[tex]\sf Energy = 800\: W \times 30\: s = 24,000\: J[/tex]
Therefore, the student uses 24,000 Joules of energy in this scenario.
[tex]\rule{200pt}{5pt}[/tex]
HELPPPP LATE HOMEWORK DUE TODAY
If F₁ has a greater magnitude than F₂, the box will accelerate backward because the net force is in the backward direction (1st option)
How do i know which direction the box will move to?To obtain the direction in which the box will move, we shall determine the net force acting on the box. This is illustrated below:
Assumption:
Magnitude of force 1 (F₁) = 40 NMagnitude of force 2 (F₂) = 25 NNet force (F) =?Net force = Magnitude of force 1 (F₁) - Magnitude of force 2 (F₂)
Net force = F₁ - F₂
Net force = 40 - 25
Net force = 15 N backward
From the above illustration, we can see that the net force is 15 N backward.
Thus, we can conclude from the box will accelerate backward (1st option)
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Bob travels 60km north turns around and travels 20km south what is his total distance travelled? what is his displacement
Explanation:
Total distance travelled is 60 + 20 = 80 km
He went 60....then turned around and headed back 20 km
so his displacement ( distance from starting point) is 60 - 20 = 40 km
What is the defining property of an mechanical wave?
A. It travels by compressing particles.
B. It travels up and down.
C. It does not need a medium to travel.
D. It needs a medium to travel.
Answer: D. It needs a medium to travel.
Explanation:
One way to categorize waves is on the basis of the direction of movement of the individual particles of the medium relative to the direction that the waves travel. Categorizing waves on this basis leads to three notable categories: transverse waves, longitudinal waves, and surface waves.
An empty cylindrical barrel is open at one end and rolls without slipping straight down a hill. The barrel has a mass of 21.0 kg, a radius of 0.260 m, and a length of 0.650 m.
The mass of the end of the barrel equals a fifth of the mass of its side, and the thickness of the barrel is negligible. The acceleration due to gravity is =9.80 m/s2.
What is the translational speed f of the barrel at the bottom of the hill if released from rest at a height of 31.0 m above the bottom?
The translational speed of the barrel at the bottom of the hill is 28.1 m/s.
What is translational speed?Translational speed is the speed of an object in a straight line. It is different from rotational speed, which is the speed of an object’s rotation. Translational speed is a measure of how quickly an object is moving in a specific direction. It is calculated by dividing the distance traveled by the time it took to travel that distance.
The barrel's initial potential energy can be calculated using the equation U = mgh, with m being the mass of the barrel (21.0 kg),
g being the acceleration due to gravity (9.80 m/s2),
and h being the height of the barrel above the bottom of the hill (31.0 m). Therefore, the barrel's initial potential energy is U = 21.0 kg × 9.80 m/s2 × 31.0 m = 6259.8 J.
At the bottom of the hill, the barrel's potential energy is zero, since it is at the lowest point.
Therefore, the barrel's total mechanical energy is equal to its kinetic energy.
Since the kinetic energy of an object is given by K = ½mv2,
where m is the mass of the barrel and v is its velocity,
we can calculate the barrel's velocity at the bottom of the hill by rearranging the equation to v = √(2K/m).
Substituting in the values for the barrel's mass (21.0 kg) and its total mechanical energy (6259.8 J) gives us v = √(2 × 6259.8 J / 21.0 kg) = 28.1 m/s.
Therefore, the translational speed of the barrel at the bottom of the hill is 28.1 m/s.
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A uniform electric field makes an angle of 60.0∘ with a flat surface. The area of the surface is 6.66×10−4m2. The resulting electric flux through the surface is 4.44 N⋅m2/C.
Calculate the magnitude of the electric field.(Express your answer with the appropriate units.)
Answer:
Explanation:
The electric flux through a surface is given by the equation:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
We are given Φ = 4.44 N⋅m2/C, A = 6.66×10−4 m2, and θ = 60.0∘. Substituting these values into the equation above and solving for E, we get:
E = Φ / (Acos(θ))
= 4.44 N⋅m2/C / (6.66×10−4 m2cos(60.0∘))
= 1.62×10^4 N/C
Therefore, the magnitude of the electric field is 1.62×10^4 N/C.
The magnitude of the electric field is 13,320 N/C.
What is electric flux?The electric flux through a surface is defined as the product of the electric field and the area of the surface projected perpendicular to the electric field. Mathematically, we can write:
Φ = EAcos(θ)
where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the surface normal.
Here in the Question,
We are given the electric flux Φ = 4.44 N·m^2/C, the area A = 6.66×10^-4 m^2, and the angle θ = 60.0°. We can solve for the magnitude of the electric field E by rearranging the equation as follows:
E = Φ / (A*cos(θ))
Substituting the given values, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*cos(60.0°))
Simplifying the denominator, we get:
E = 4.44 N·m^2/C / (6.66×10^-4 m^2*0.5)
E = 13,320 N/C
Therefore, 13,320 N/C is the magnitude of the electric field.
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Express your answer with the appropriate units. A 60.0 kg box hangs from a rope. What is the tension in the rope if:
A. The box is at rest?
B. The box moves up a steady 4.80 m/s ?
C. The box has vy = 5.00 m/s and is speeding up at 5.40 m/s^2 ? The y axis points upward.
D. The box has vy = 5.00 m/s and is slowing down at 5.40 m/s^2 ?
When the box is at rest, the tension in the rope is equal to the weight of the box. The tension in the rope is 588 N.
What is tension in physics?In physics, tension refers to the pulling force that is transmitted through a string, cable, rope, etc when it is pulled tight by forces acting at both ends. Tension is a vector quantity, and measured in units of newtons (N) or pounds (lbs).
A. When the box is at rest, the tension in the rope is equal to the weight of the box, which is given by:
Tension = Weight of the box = mg = (60.0 kg)*(9.81 m/s²) = 588 N
Thus, the tension = 588 N.
B. When the box moves up at a steady 4.80 m/s, the tension in the rope is equal to the force required to lift the box against gravity, which is given by:
Tension = Weight of the box + Force to lift the box = mg + ma = (60.0 kg)*(9.81 m/s²) + (60.0 kg)*(4.80 m/s²) = 1,167.6 N
Therefore, the tension in the rope is 1,167.6 N.
C. When the box has velocity along the y-axis = 5.00 m/s and is speeding up at 5.40 m/s², the tension in the rope is given by the equation:
Tension = Weight of the box + Force to accelerate the box = mg + ma = (60.0 kg)*(9.81 m/s²) + (60.0 kg)*(5.40 m/s²) = 1,199.4 N
Therefore, the tension in the rope is 1,199.4 N.
D. When the box has velocity along y-axis = 5.00 m/s and is slowing down at 5.40 m/s², the tension in the rope is given by the equation:
Tension = Weight of the box - Force to decelerate the box = mg - ma = (60.0 kg)(9.81 m/s²) - (60.0 kg)(5.40 m/s²) = 981.6 N
Therefore, the tension in the rope is 981.6 N.
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A harp string has a length of 30.5 cm and vibrates with a node at each end and an antinode inthe center. If its frequency is 440 Hz, find (a) the wavelength and (b) the speed of the waves on the string.
Answer:
In this problem, the harp string is fixed at both ends, so it is a standing wave with nodes at both ends and an antinode in the center. The frequency of the wave is given as 440 Hz, and the length of the string is 30.5 cm.
(a) To find the wavelength of the wave, we can use the formula:
λ = 2L/n
where λ is the wavelength, L is the length of the string, and n is the number of nodes. In this case, n = 2 (since there are nodes at both ends) and L = 30.5 cm, so we have:
λ = 2(30.5 cm)/2 = 30.5 cm
Therefore, the wavelength of the wave is 30.5 cm.
(b) To find the speed of the wave on the string, we can use the formula:
v = fλ
where v is the speed of the wave, f is the frequency of the wave, and λ is the wavelength. In this case, f = 440 Hz and λ = 30.5 cm, so we have:
v = (440 Hz)(30.5 cm) = 13420 cm/s
Therefore, the speed of the wave on the string is 13420 cm/s
Explanation:
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Use the data in the table to determine the identities of the two gasses that you found could be components of water. Provide evidence to support your claim.
The two gases that could be components of water are indeed hydrogen and oxygen.
Evidence to support this claim:
1. The chemical formula for water is H2O, which means that it is composed of two hydrogen atoms and one oxygen atom.
2. The table of elements shows that hydrogen (H) and oxygen (O) are both elements that exist in nature.
3. The atomic mass of hydrogen (1.008) and oxygen (15.999) matches the molecular mass of water (18.015).
4. Water is produced when hydrogen gas (H2) is burned in the presence of oxygen gas (O2), according to the following equation: 2H2 + O2 → 2H2O.
Overall, the evidence supports the conclusion that hydrogen and oxygen are the two gases that could be components of water.
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Gas pressure is defined as
Select one:
O a. mass per unit area
O b.
O c. force per unit area
O d. force per unit volume
acceleration per unit volume
Answer: b. force per unit area.
Explanation:
6. An 8000.0 kg truck starts off from rest and reaches a velocity of 18.0 m/s in 6.00 seconds. What is the truck’s acceleration and how much momentum does it have after it has reached this final velocity?
The truck's acceleration is 3.0m/s² and the momentum of the truck is 144000 kg m/s.
What is acceleration?It is the rate at which the speed and direction of a moving object vary over time.
We can use the following equation to calculate the acceleration of the truck:
a = (v - u) / t
where
a = acceleration
v = final velocity = 18.0 m/s
u = initial velocity = 0 m/s (the truck starts from rest)
t = time taken = 6.00 s
Substituting the values, we get:
a = (18.0 m/s - 0 m/s) / 6.00 s
a = 3.00 m/s²
Therefore, the acceleration of the truck is 3.00 m/s².
We can use the following equation to calculate the momentum of the truck:
p = m * v
where
p = momentum
m = mass of the truck = 8000.0 kg
v = final velocity = 18.0 m/s
Substituting the values, we get:
p = 8000.0 kg * 18.0 m/s
p = 144000 kg m/s
Therefore, the momentum of the truck after it has reached its final velocity is 144000 kg m/s.
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Two asteroids are suspended in space 50 meters apart. The masses of the asteroids are 2000000 kg and
3000000 kg.
Answer:
Explanation:
What is the gravitational force between them?
To calculate the gravitational force between two objects, we can use the formula:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.6743 x 10^-11 N * m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between them.
Plugging in the given values, we get:
F = (6.6743 x 10^-11 N * m^2 / kg^2) * (2000000 kg) * (3000000 kg) / (50 m)^2
F = 0.8046 N
Therefore, the gravitational force between the two asteroids is approximately 0.8046 N.
State each of Newton's Laws of Motion and explain how each can be observed during the flight of a space craft, from liftoff until the craft enters space.
newton 3th law of motion and newton's law of universal gravitation
Answer: 1. Newton's First Law of Motion (Law of Inertia): An object at rest will remain at rest, and an object in motion will remain in motion with a constant velocity unless acted upon by an external force.
During liftoff, the spacecraft is initially at rest. However, the rocket engines generate a force that propels the spacecraft forward and overcomes its initial state of rest. Once the spacecraft is in motion, it will continue to move forward with a constant velocity unless acted upon by other external forces, such as air resistance or gravity.
2. Newton's Second Law of Motion: The acceleration of an object is directly proportional to the force applied to it, and inversely proportional to its mass.
As the rocket engines burn fuel, they generate a force that propels the spacecraft forward. The acceleration of the spacecraft is directly proportional to the force generated by the engines, and inversely proportional to the mass of the spacecraft. As fuel is consumed and the spacecraft becomes lighter, its acceleration will increase, allowing it to reach escape velocity and enter space.
3. Newton's Third Law of Motion: For every action, there is an equal and opposite reaction.
During liftoff, the rocket engines generate a powerful force that propels the spacecraft forward. However, the engines also generate an equal and opposite reaction force, pushing back against the rocket and causing it to shake and vibrate. This force is also responsible for the loud noise and exhaust plumes that are visible during liftoff.
These are the three laws of motion developed by Sir Isaac Newton, and they explain how objects move and interact with one another. They can be observed in the launch and flight of a spacecraft, from the initial state of rest to the forces that drive it forward, to the equal and opposite forces that shake the rocket during liftoff.
It is fun to exercise outside, but you have to be careful when it's hot. What are two things you should always do when you exercise in the heat?
Answer:
When exercising in the heat, it's important to take precautions to prevent heat-related illnesses. Two things you should always do when exercising in the heat are:
1.Stay hydrated: Drink plenty of water before, during, and after your workout to avoid dehydration. Sip water frequently, even if you don't feel thirsty.
2.Take breaks and rest in the shade: If you start feeling dizzy, lightheaded, or excessively fatigued, take a break in a cool, shaded area. Resting can help your body cool down and prevent heat exhaustion or heat stroke.
Explanation:
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What factors would create an ideal circuit?
An ideal circuit is a theoretical representation of an electrical circuit, where all components are perfect and all parameters such as resistance, capacitance, and inductance are zero.
The ideal circuit also has no energy losses, making it an ideal electrical system. To create an ideal circuit, the following factors must be considered:
1. Perfectly Conductive Wires: The wires and other conductors used in the circuit should be perfect conductors, which means the resistance should be zero. This will ensure that no energy is lost in the form of heat.
2. Zero Inductance: Inductance is a property of a circuit which causes a voltage drop when current flows through it. The ideal circuit should have no inductance so that the current can flow freely.
3. Zero Capacitance: Capacitance is a property in which electric charge builds up when current passes through it. To create an ideal circuit, the capacitance should be zero.
4. Zero Impedance: Impedance is the opposition to the flow of current in an electrical circuit. The ideal circuit should have zero impedance so that the current can flow freely.
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A gas is contained in a cylinder with a frictionless moveable piston at a pressure of 2.7 * 105 pascals and a volume of 0.04 cubic meters. What is the work done by the gaseous system if the volume is increased to 0.12 cubic meters ?
The work done by the gaseous system if the volume is increased to 0.12 cubic meters is given as 21,600 joules
How to solve for the workdoneTo find the work done by the gas, we can use the formula:
W = PΔV
where W is the work done, P is the pressure of the gas, and ΔV is the change in volume.
At the initial state, the pressure is P = 2.7 × 10^5 Pa and the volume is V1 = 0.04 m^3. At the final state, the volume is V2 = 0.12 m^3.
The change in volume is ΔV = V2 - V1 = 0.12 m^3 - 0.04 m^3 = 0.08 m^3.
Substituting these values into the formula, we get:
W = PΔV = (2.7 × 10^5 Pa) × (0.08 m^3) = 21,600 J
Therefore, the work done by the gaseous system is 21,600 joules (J).
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Answer:
4.6x10^4 joules
Explanation:
waves are generated in a rope of length 6m. What is the speed of the wave if its period is 25.m
The speed of the wave would be0.48 m/s.
Speed of a waveThe speed of a wave is given by the formula:
v = λ/T
where v is the wave speed, λ (lambda) is the wavelength, and T is the period.
To solve this problem, we need to know the wavelength of the wave. We can find the wavelength using the formula:
λ = 2L
where L is the length of the rope. Substituting L = 6 m, we get:
λ = 2 × 6 m = 12 m
Now we can use the formula for wave speed:
v = λ/T
Substituting λ = 12 m and T = 25 s, we get:
v = 12 m/25 s = 0.48 m/s
Therefore, the speed of the wave is 0.48 m/s.
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When a ball is thrown into the air, its kinetic energy is lowest
A at its highest point.
B. at the moment it is released.
C. as it begins to fall back to the ground.
A rock with a mass of 10.0 kg is balanced on top of a large boulder. Describe the forces acting on the rock, and use the concept of forces to explain why it stays on top of the boulder.
There are two forces acting on the rock: the force of gravity pulling it downward and the force of the boulder supporting it from underneath.
What is the force of gravity?The force of gravity is the gravitational attraction between the rock and the Earth. It pulls the rock downward with a force equal to its weight, which is given by the equation Fg = mg, where Fg is the force of gravity, m is the mass of the rock, and g is the acceleration due to gravity (approximately 9.81 m/s^2).
Why do boulder stays on top?The concept of forces explains why the rock stays on top of the boulder because the forces are balanced. The force of gravity pulling the rock downward is equal and opposite to the force of the boulder supporting it from underneath. As a result, the rock remains in equilibrium, or a state of balance, on top of the boulder. If either force were to change, the equilibrium would be disrupted, and the rock would either fall to the ground or be pushed off the boulder.
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an object is launched at a velocity of 40m/s in a direction making an angle of 50°upward with the horizontal
a)what is the maximum height reached by the object
b) what is the object total flight time between launch and touching the ground
c) what's the object horizontal range(maximum ×above ground)
a metal block of density 900kg weight 60newton in air find it's weight when it is immersed in paraffin wax of density 800kg
Answer:
We can use the concept of buoyancy to solve this problem.
The weight of the metal block in air is equal to the force of gravity acting on it, which is given as 60 Newtons. When the block is immersed in paraffin wax, it displaces a certain volume of wax equal to its own volume, and experiences an upward force due to buoyancy that partially cancels out the force of gravity acting on it.
The buoyant force acting on the block is given by the formula:
buoyant force = weight of fluid displaced
= density of fluid x volume of fluid displaced x acceleration due to gravity
The weight of the metal block in the paraffin wax is then equal to the difference between the weight of the block in air and the buoyant force acting on it.
Let's calculate the volume of the metal block first:
density of metal block = 900 kg/m³
weight of metal block in air = 60 N
acceleration due to gravity = 9.81 m/s²
weight of metal block = density of metal block x volume of metal block x acceleration due to gravity
volume of metal block = weight of metal block / (density of metal block x acceleration due to gravity)
= 60 N / (900 kg/m³ x 9.81 m/s²)
= 0.006536 m³
Now, let's calculate the weight of the metal block in the paraffin wax:
density of paraffin wax = 800 kg/m³
buoyant force = density of fluid x volume of fluid displaced x acceleration due to gravity
= 800 kg/m³ x 0.006536 m³ x 9.81 m/s²
= 51.02 N
weight of metal block in paraffin wax = weight of metal block in air - buoyant force
= 60 N - 51.02 N
= 8.98 N
Therefore, the weight of the metal block when it is immersed in paraffin wax of density 800 kg/m³ is 8.98 Newtons.
If a 9 V battery is connect to a 4 ohm resistor, what is the current?
O2.3 A
O 36 A
O 0.44 A
5 A
Answer: Given data
The resistance of the first resistor is R1 = 4 ohm
The resistance of the second resistor is R2 = 5 ohm
The potential difference of the battery is V = 9 V
The resistors are connected in series. The expression for the equivalent resistance is given as:
The expression for the current in the 4-ohm resistor is given as:
Thus, the magnitude of the current flows through the 4-ohm resistor is 1 A.
Explanation:
a mass of 20kg is held stationary by a rope passing over a frictionless pally. what is the tension T in the rope?
The tension in the rope is 196.2 N. The rope is exerting a force of 196.2 N on the object to keep it stationary.
Assuming that the mass is not accelerating, the tension in the rope must be equal to the weight of the mass. The weight of the mass can be found using the formula:
weight = mass x acceleration due to gravity
where acceleration due to gravity is approximately 9.81 m/s².
Therefore, the weight of the mass is:
weight = 20 kg x 9.81 m/s² = 196.2 N
Since the mass is held stationary, the tension in the rope must be equal to the weight of the mass, which is 196.2 N. So the tension T in the rope is 196.2 N.
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A 300 g football is kicked with an initial velocity of 140 m/s in a direction that
makes a 30° angle with the horizon. Find the peak height of the football.
Answer:
Explanation:
Assuming that air resistance is negligible, we can use the following kinematic equations to solve for the peak height:
v_f^2 = v_i^2 + 2ad
where v_f = 0 m/s (at the peak height) and a = -9.8 m/s^2 (acceleration due to gravity)
and
d = v_i t + (1/2)at^2
where d is the displacement or the peak height we want to find, v_i is the initial velocity, t is the time it takes to reach the peak height.
First, we need to resolve the initial velocity into its vertical and horizontal components:
v_i_x = v_i cos(30°) = 121.1 m/s
v_i_y = v_i sin(30°) = 70.0 m/s
Next, we can use the vertical component of the initial velocity to find the time it takes to reach the peak height:
v_f = v_i_y + at
0 m/s = 70.0 m/s + (-9.8 m/s^2)t
t = 7.14 s
Finally, we can use the time we found and the kinematic equation for displacement to find the peak height:
d = v_i_y t + (1/2)at^2
d = (70.0 m/s)(7.14 s) + (1/2)(-9.8 m/s^2)(7.14 s)^2
d = 247.5 m
Therefore, the peak height of the football is 247.5 meters.
an electron of hydrogen is present in the 3.4eV energy state find angular momentum of electron
To find the angular momentum of an electron in the hydrogen atom, we can use the formula:
L = n * h / (2 * π)
where L is the angular momentum, n is the principal quantum number, h is Planck's constant, and π is a mathematical constant approximately equal to 3.14159.
First, we need to determine the value of n for the electron in the 3.4 eV energy state. We can use the formula for the energy of an electron in a hydrogen atom:
E = -13.6 eV / n^2
where E is the energy of the electron and -13.6 eV is the energy of the electron in the ground state of the hydrogen atom.
Solving for n, we get:
n^2 = (-13.6 eV) / E
n^2 = (-13.6 eV) / (3.4 eV)
n^2 = 4
n = 2
Therefore, the electron is in the second energy level of the hydrogen atom.
Now, we can calculate the angular momentum using the formula above. Substituting the values, we get:
L = 2 * h / (2 * π)
L = h / π
We can approximate π as 3.14159 and use the value of Planck's constant as h = 6.626 x 10^-34 J s. Substituting these values, we get:
L = (6.626 x 10^-34 J s) / (3.14159)
L = 2.104 x 10^-34 J s
Therefore, the angular momentum of the electron in the second energy level of the hydrogen atom is 2.104 x 10^-34 J s.