The battery with a lifetime of 14.5 hours is at the 40.13th percentile in terms of battery lifetimes, assuming a normal distribution with a mean of 15 hours and a standard deviation of 2 hours.
Certainly, to find the percentile of the battery's lifetime, we'll use the Z-score formula and then refer to the standard normal distribution table. Let's assume a normal distribution with a mean (μ) of 15 hours and a standard deviation (σ) of 2 hours. The battery's lifetime is X = 14.5 hours.
The Z-score is calculated as:
Z = (X - μ) / σ
Substitute the values:
Z = (14.5 - 15) / 2 = -0.25
Now, we need to find the percentile associated with this Z-score. Looking up -0.25 in the standard normal distribution table, we find that the corresponding percentile is approximately 40.13%.
The question probable may be:
What is the percentile of a battery's lifetime with a mean (μ) of 15 hours and a standard deviation (σ) of 2 hours when its actual lifetime is X = 14.5 hours? Use the Z-score formula and the standard normal distribution table to determine the percentile associated with the Z-score of -0.25.
This battery's lifetime falls in the 22.66th percentile.
The lifetime of a battery is normally distributed with a mean (μ) of 16 hours and a standard deviation (σ) of 2 hours. To find what percentile a particular battery lasting 14.5 hours falls into, we need to calculate its Z-score.
The Z-score is given by:
[tex]Z = \frac{X- \mu}{\sigma}[/tex]
where X is the observed value.
The Z-score of the given battery is:
Z = [tex]\frac{14.5 - 16}{2}[/tex] = [tex]\frac{-1.5}{2}[/tex] = - 0.75
According to the Z-table, a Z-score of - 0.75 corresponds to a cumulative probability of approximately 0.2266.
This means that 14.5 hours is at the 22.66th percentile.
Thus, the lifetime of a particular battery lasting 14.5 hours falls at the 22.66th percentile of the lifetime distribution.
The complete question is:
The lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.
Activities:
What is the probability that a battery will last more than 19 hours?Find the 10th percentile of the lifetimes.A particular battery lasts 14.5 hours. What percentile is its lifetime on?What is the probability that the lifetime of a battery is between 14.5 and 17 hours?Latent heat of fusion refers to which changes of state?
Answer:
Explanation:
The amount of energy required to change the state of matter at constant temperature is called latent heat.
There are two types of latent heat.
1. Latent heat of fusion: The amount of heat required to convert 1 kg of ice at 0 degree Celsius into 1 kg water at 0 degree Celsius is called latent heat of fusion.
2. Latent heat of vaporization: The amount of heat required to convert 1 kg of water at 100 degree Celsius into 1 kg steam at 100 degree Celsius is called latent heat of vaporization.
It takes Harry 34 s to walk from x1 = -11 m to x2 = -54 m .
In the equation for centripetal force, which expression represents the centripetal acceleration of the object?
Answer:
v^2/r
Explanation:
Took the review
The pilot of an airplane traveling 180km/h wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?
To calculate the time the supplies should be dropped before the plane is directly overhead, use the equation for free-fall motion and plug in the values given. The supplies should be dropped approximately 5.06 seconds before the plane is directly overhead.
Explanation:To determine how many seconds before the plane is directly overhead the supplies should be dropped, we need to calculate the time it takes for the supplies to fall 160 m. We can use the equation for free-fall motion:
Time = sqrt((2 * distance) / g)
where distance is the height the supplies need to fall and g is the acceleration due to gravity. Plugging in the values, we get:
Time = sqrt((2 * 160 m) / 9.8 m/s²) ≈ 5.06 seconds
Therefore, the supplies should be dropped approximately 5.06 seconds before the plane is directly overhead.
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The ____ value of the overflow style keeps the element at the specified height and width, but cuts off excess content.
a. hidden
b. visible
c. scroll
d. auto
Answer:
The correct answer is A. The hidden value of the overflow style keeps the element at the specified height and width, but cuts off excess content.
Explanation:
Hidden variable theories are interpretations of quantum physics, which means that a quantum mechanical system cannot be fully described by a wave function, but at least one additional variable is needed.
Hidden values would give unambiguous value to the properties of a quantum mechanical particle - position, amount of motion and energy - whether observed or not. During the evolution of quantum physics, hidden variables were advocated by, among others, Albert Einstein, but today, especially after the presentation of Bell's theorem, they have weak support among physicists. The only such theory that is still minimally shown with interest is Bohemian mechanics, which uses non-local hidden variables.
If you were creating an electrical circuit and ran out of wire what materials would you use
A:yarn
B:licorice strings
C:plastic knitting needle
D:tin foil
A football is kicked from a tee at 12 m/s at 72° above the horizontal. What is the maximum height of the football
The maximum height of the football when kicked from a tee at 12 m/s at an angle of 72° above the horizontal is approximately 11.89 meters.
Explanation:To solve this problem, we will use the equation of motion that describes vertical displacement: h = vi sinθ t - 0.5gt2, where vi is the initial velocity, θ is the angle it was fired at, and g is the acceleration due to gravity. The maximum height is reached when the ball is momentarily stationary, in other words when the time, t, equals the time it takes for the ball to ascend (vi sinθ/g).
Substituting these values into our equation, we get: h = 12 sin(72°)*12 sin(72°)/9.8 - 0.5*9.8*(12 sin(72°)/9.8)2.
This results in a maximum height of approximately 11.89 meters.
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A wave travels through water at a speed of 3 m/s and has a frequency of 10 Hz. What is the wavelength of the wave?
V=wavelength*frequency
3 m/s=wavelength*10 Hz
3m/s=10 Hz
wavelength= .3
Answer:
Wavelength of the wave, λ = 0.3 m
Explanation:
It is given that,
The speed of the wave, v = 3 m/s
The frequency of the wave, f = 10 Hz
We know the relationship between the frequency, wavelength and the speed of the wave. Mathematically, it can be written as :
[tex]speed=frequency\times lambda[/tex]
or
[tex]v=f\times \lambda[/tex]
[tex]\lambda=\dfrac{v}{f}[/tex]
[tex]\lambda=\dfrac{3\ m/s}{10\ Hz}[/tex]
[tex]\lambda=0.3\ m[/tex]
Hence, the wavelength of the wave is 0.3 m
A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 ∘ incline. after sliding down the 110-m long incline (on which the coefficient of kinetic friction is μk = 0.18), the snowboarder has attained a velocity v. the snowboarder then slides along a flat surface (on which μk = 0.15) and comes to rest after a distance x. part a use newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface.
Acceleration on the inclined plane and flat surface is different. The acceleration of snowboarding on the inclined plane is 3.05 m/sec² while on the flat surface is 1.4715 m/sec².
What is the friction force?It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N).
Mathematically it is defined as the product of the coefficient of friction and normal reaction.
(a)
On resolving the given force and accelertaion in the different components and balancing the equation gets.
Components in the x-direction
mgsina-F= ma
mgcosa=R
F=μR
F = μmgcosa
mg(sina-μcosa)=ma
a=g(sina-μcosa)
a=9.31(sin28°-0.18cos28°)
a= 3.05 m/sec²
Hence acceleration of snowboarding on the inclined plane is 3.05 m/sec²
(b)
According to Newton's third equation of motion;
v²=u²+2as
v²= (5)²+2×3.05×110
v=26.4 m/sec.
Fₓ×f= mgμ=ma
a=g×μ
a=9.81×0.15
a= 1.47 m/sec²
Hence acceleration on the flat surface is 1.4715 m/sec².
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Solid-state storage is quickly replacing forms of _____ on small devices like the ipod.
On a beautiful night in Washington D.C., you see a mirror image of the Washington Monument and surrounding scenery. What causes this mirror image?
A. Absorbed light
B. Reflected light
C. White light
D. Refracted light
5.3 × 1012 kg satellite is 1,800 m from another satellite that has a mass of 3.5 × 108 kg. What is the gravitational force between the satellites? 3.82 × 104 N 6.87 × 107 N 5.72 × 1014 N 1.03 × 1018 N
The answer is: 3.82 × 10^4 N. Hope this helps!
You're riding a unicorn at 25 m/s and come to a uniform stop at a red light 20m away. What's your acceleration?
The answer is -15.625m/s².
Acceleration is the change in velocity over a period of time. It can be computed using the formula:
[tex] a = \dfrac{vf-vi}{t} [/tex]
Where:
vf = final velocity
vi = initial velocity
t = time
Now let's see what was given in your problem:
The car was moving at 25m/s and then came to a stop. So initially it was moving and then it stopped. This means the final velocity will be 0m/s because it stopped moving.
But look at the problem, it shows no time. We need to solve for time from the time it moved till it reached the red light 20 m away.
Time can be computed using the kinematics formula:
[tex] d = \dfrac{vi+vf}{2} *t[/tex]
We just derive the formula from the equation by filling out what we know first.
[tex] 20m = \dfrac{25m/s+0m/s}{2}(t)[/tex][tex] 20m = 12.5m/s{2}(t)[/tex]
The time it took from the point it was moving till it stopped is 1.6s. We can now use this in our acceleration formula.
[tex] a = \dfrac{0m/s-25m/s}{1.6s} [/tex]
[tex] a = \dfrac{-25m/s}{1.6s} [/tex]
[tex] a = -15.625m/s^{2} [/tex]
Notice that the acceleration is negative. This means that the car decelerated or slowed down.
Answer:
My acceleration is 15.63 m/s² (slowing down)
Explanation:
The expression for the acceleration is equal:
[tex]v^{2} _{f} -v^{2} _{i} =2ax[/tex]
Where
vi = initial speed = 25 m/s
vf = final speed = 0
x = displacement = 20 m
Replacing and clearing the acceleration "a":
[tex]a=\frac{v^{2} _{f} -v^{2} _{i} }{2x} =\frac{0-25^{2} }{2*20} =--15.63m/s^{2}[/tex]
The negative sign of acceleration means that it is slowing down
The cone cells of the human eye are sensitive to three wavelength ranges, which the eye interprets as blue (419nm), green (531 nm), and red(558nm). if the optic nerve in the eye requires 2.0x10^-17j of energy to initiate the sight impulses to the brain, how many photons of blue light, green light, and red
The number of photons of blue light required is 42 photons of blue light
The number of photons of green light required is 53 photons of green light
The number of photons of red light required is 56 photons of red light
The energy of one photon of light is calculated using the formula:
E = h * c / λ
where h, Planck's constant = 6.63 * 10⁻³⁴ Js
speed of light c = 3 * 10⁸ m/s
λ = wavelength of light
wavelength of blue light = 419 nm = 4.19 * 10⁻⁷ m
wavelength of green light = 531 nm = 5.31 * 10⁻⁷ m
wavelength of red light = 558 nm = 5.58 * 10⁻⁷ m
Number of photons of light = Energy of light / Energy of one photon of light
Energy of light required by optic nerve = 2.0 * 10⁻¹⁷ J
Energy of one photon of blue light,
E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 4.19 * 10⁻⁷ m = 4.74 * 10⁻¹⁹ J
Number of photons of blue light = 2.0 * 10⁻¹⁷ J / 4.74 * 10⁻¹⁹ J
Number of photons of blue light = 42 photons of blue light
Energy of one photon of green light,
E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.31 * 10⁻⁷ m = 3.74 * 10⁻¹⁹ J
Number of photons of green light = 2.0 * 10⁻¹⁷ J / 3.74 * 10⁻¹⁹ J
Number of photons of green light = 53 photons of green light
Energy of one photon of red light,
E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.58 * 10⁻⁷ m = 3.56 * 10⁻¹⁹ J
Number of photons of red light = 2.0 * 10⁻¹⁷ J / 3.56 * 10⁻¹⁹ J
Number of photons of red light = 56 photons of red light
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Andy has two strong magnetic marbles of equal size. What will happen when he puts the two marbles about 2 centimeters apart?
You are learning about energy transformations in science class. Today, you are making a solar oven in science class. Your group's reward? You are going to use your solar oven to make s'mores: graham crackers, toasted marshmallows, and melted chocolate. When you have completed your oven, you get to eat the s'mores! Your oven converts solar energy into ___________ energy to make the s'mores.
A) cooked
B) heat
C) light
Eliminate
D) mechanical
Answer:
B) HEAT ENERGY
Explanation:
I hope this is helpful you guys deserve the support
When you have completed your oven, you get to eat the s'mores! Your oven converts solar energy into heat energy to make the s'mores. Therefore, option B is correct.
What is heat energy ?The movement of minuscule atoms, molecules, or ions in solids, liquids, and gases produces heat energy. From one thing to another, heat energy can be exchanged. Heat is the flow or transfer that occurs as a result of the temperature differential between two objects.
Radiation is used to cook the s'mores in the solar oven that is created in this exercise. When heat is passed between two objects (the sun and the s'mores) without having direct touch, this is known as radiation. Electromagnetic waves that move through the air transfer the heat.
Heat is created when visible and ultraviolet high frequency light transforms into low frequency infrared energy.
Thus, option B is correct.
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Whenever two apollo astronauts were on the surface of the moon, a third astronaut orbited the moon. assume the orbit to be circular and 430 km above the surface of the moon, where the acceleration due to gravity is 1.08 m/s2. the radius of the moon is 1.70 â 106 m?
The gravitational force between Earth and the Sun is a two-way force. Both the planet and the Sun attract each other. However, Earth revolves around the Sun rather than the Sun revolving around Earth. Which statement BEST explains the orbit of the Earth around the Sun? A) The Sun is at the center of the Solar System. B) The Sun’s mass is much greater than Earth’s. C) Earth rotates about its axis, but the Sun does not. D) Other planets also try to move the Sun around them.
The correct choice would be
B) The Sun’s mass is much greater than Earth’s
The sun as we know has greatest mass in our solar system and lighter objects tends to orbit around the heavier objects. the mass of earth is very much smaller as compared to that of the sun. hence the earth orbits around the sun due to the force of gravitational attraction between the two objects.
Answer:
B. The sun's mass is much greater than Earth's.
Explanation:
I got it right on UsaTestPrep
Hope this helps!
From: Aug1e
Which of these best explains the ability of small insects to walk on the surface of still water?
The ability of small insects to walk on water is due to surface tension, which results from cohesive forces among water molecules. This tension creates a thin 'skin' at the water's surface that can support the weight of light objects, such as insects.
The ability of small insects to walk on the surface of still water can be best explained by the phenomenon of surface tension. Surface tension is created due to the cohesive forces between water molecules at the liquid-air interface. This cohesion results in a thin 'skin' forming at the surface, which can support the weight of small insects like water striders. These insects distribute their weight over their long legs, ensuring that the force they exert is less than the surface tension holding the water molecules together, allowing them to effectively 'walk' on water.
An example of this can be seen when a paper clip or a thin razor blade is carefully placed on the surface of water without sinking, demonstrating the strength of surface tension.
Find the momentum p, in the laboratory frame of reference, of a proton moving with a speed of 0.805
c. use 938mev/c2 for the mass of a proton.
Explanation of how to calculate the momentum of a proton moving at 0.805c using the relativistic momentum formula.
The momentum (p) of a proton moving at 0.805c can be calculated using the relativistic momentum formula:
[tex]p = (m * v) / \sqrt{(1 - v^2 / c^2)[/tex]
Substitute the mass of a proton (938 MeV/c^2), the velocity (0.805c), and the speed of light (3 x 10^8 m/s) into the formula to find the momentum value.
An air-gap parallel plate capacitor of capacitance c0 = 20 nf is connected to a battery with voltage v = 12 v. while the capacitor remains connected to the battery, we insert a dielectric (κ = 2.6) into the gap of the capacitor, filling one half of the volume as shown below. what is u, the energy stored in the this capacitor?
Answer:
3.7 * 10[tex]^{-5} J[/tex]
Explanation:
Thinking process:
Let the energy be calculated by the following:
[tex]U = \frac{1}{2}CV^{2}[/tex]
where V is the voltage applied across the load.
C is the capacitance
In case of a dielectric, the capacitance is given by the following equation:
[tex]C = kC_{0}[/tex]
where [tex]C_{0}[/tex] is the capacitance in vacuum. So, the energy stored becomes:
[tex]U = \frac{1}{2} (kC_{o})V^{2}[/tex]
Then, k = 2.6 , [tex]C_{0} = 20 nF[/tex], and V = 12 V
Therefore, in the problem, the energy stored becomes:
[tex]U = \frac{1}{2} (2.6 * 20*10^{-9}) (12)^{2} \\ = 3.7 * 10^{-5} J[/tex]
A circular disk has surface charge density 24 nc/cm2 what will the surface charge density be if the radius of the disk is doubled?
One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 2.51 km. they start at the west side of the lake and head due south to begin with. (a) what is the distance they travel? (b) what is the magnitude of the couple's displacement? (c) what is the direction (relative to due east) of the couple's displacement?
day and night are cause by earth's revolution on its axis true or false
FALSE, the earth's rotation on its axis does not cause night and day. The rotation of the earth is responsible for the occurrence of night and day.
What is the earth's rotation?Revolution and rotation are the terms that describe the different movements of the earth. The movement of the earth on its axis is known as rotation.
Revolution is the movement of the earth around the sun in a fixed route or orbit. The earth's axis, which is an imaginary line, forms a 6612° angle with its orbital plane.
The earth's rotation on its axis does not cause night and day. The rotation of the earth is responsible for the occurrence of night and day.
Hence, the given statement is false.
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Two hockey pucks with mass 0.1 kg slide across the ice and collide. Before the collision, puck 1 is going 15 m/s to the east and puck 2 is going 12 m/s to the west. After the collision, puck 2 is going 15 m/s to the east. What is the velocity of puck 1?
Final answer:
Using the conservation of momentum, the final velocity of puck 1 after the collision is determined to be 1.2 m/s to the west.
Explanation:
The student's question is about determining the velocity of puck 1 after a collision in an ice hockey game. Since momentum is conserved in collisions, we can use the law of conservation of momentum to find the answer. Puck 1 has a mass of 0.1 kg and is initially traveling at 15 m/s to the east, whereas puck 2, also 0.1 kg, is initially going 12 m/s to the west. After the collision, puck 2 is moving at 15 m/s to the east. We can set up the equation for conservation of momentum as follows:
Initial Momentum = Final Momentum
(m1 * v1_initial) + (m2 * v2_initial) = (m1 * v1_final) + (m2 * v2_final)
Plugging in the given values and solving for v1_final (velocity of puck 1 after the collision):
(0.1 kg * 15 m/s) + (0.1 kg * -12 m/s) = (0.1 kg * v1_final) + (0.1 kg * 15 m/s)
Simplifying the equation:
1.5 kg*m/s -1.2 kg*m/s = 0.1 kg * v1_final + 1.5 kg*m/s
Rearranging to solve for v1_final gives:
v1_final = (1.5 kg*m/s - 1.2 kg*m/s - 1.5 kg*m/s) / 0.1 kg
Calculating v1_final:
v1_final = -1.2 m/s
Therefore, after the collision, puck 1 is moving at a velocity of 1.2 m/s to the west.
List at least 3 physical properties that the professor describes of his newly discovered flubber
Answer:
Flubber is a combination of two words Fluid+ Rubber. It means flubber has physical properties of both fluid and rubber(solid).
Physical properties of Flubber are as follows
1. It has elasticity like rubber
2. It can take the shape of the container in which it is filled. It does not have any particular shape like fluid.
3.It has viscoplastic nature
4. It is gelatinous
5. It flows under low pressure and can break when high pressure is applied on it.
A spring-loaded piston-cylinder device is filled with 0.35 kg of water vapor that is initially at 4 mpa and 4000c. initially, the spring exerts no force against the piston. the spring constant in the spring-force relationship is k = 0.75 and the piston diameter is d = 20 cm. the water now undergoes a process until its volume is one-half of the original volume. calculate the final temperature and the specific enthalpy of the water.
To accurately calculate the final temperature and the specific enthalpy of the water vapor in the given spring-loaded piston-cylinder device after the water volume is reduced to half, we'd require the use of steam tables or equations of state and a clear understanding of the thermodynamic process involved.
Explanation:The spring-loaded piston-cylinder device question given is based on the principles of thermodynamics and requires calculating the final temperature and the specific enthalpy of water after it undergoes a process where its volume is halved. To solve this problem, one can use the steam tables alongside the principles of thermodynamic processes involving an ideal gas or a real substance such as water, depending on the provided properties and the specified conditions.
To calculate the final temperature and specific enthalpy, we would need more details such as the properties of the water vapor at its initial state (using steam tables or equations of state, for example) and the characteristics of the thermodynamic process (constant pressure, isothermal, adiabatic, etc.). Moreover, if the properties are not sufficient to solve analytically, we might utilize software or further data from thermodynamic tables to aid in solving this question.
Without additional information about the specific heat capacities or the relationship between pressure and temperature for the water vapor, it is challenging to provide an accurate answer to the student's question.
The moon clearly exhibits a light and dark portion during most of the month except during full moon. What causes the dark portion of any phase to change in size, that is, become either more or less black ?
On its own, a certain tow-truck has a maximum acceleration of 3.0 m/s2. what would be the maximum acceleration when this truck was towing a bus of twice its own mass?
The maximum acceleration would be 1.0 m/s² when this truck was towing a bus of twice its own mass
[tex]\texttt{ }[/tex]
Further explanationNewton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
Given:
initial acceleration = a₁ = 3.0 m/s²
mass of tow-truck = m₁ = m
mass of bus = m₂ = 2m
Asked:
final acceleration = a₂ = ?
Solution:
[tex]\texttt{Initial Force of Tow-Truck = Final Force of Tow-Truck }[/tex]
[tex]F_1 = F_2[/tex]
[tex]m_1 a_1 = m_2 a_2[/tex]
[tex]m (3.0) = (m + 2m) a_2[/tex]
[tex]3m = 3m (a_2)[/tex]
[tex]a_2 = 3m \div 3m[/tex]
[tex]\boxed{a_2 = 1.0 ~ \mathtt{ m/s^2}}[/tex]
[tex]\texttt{ }[/tex]
Conclusion :The maximum acceleration would be 1.0 m/s²
[tex]\texttt{ }[/tex]
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Answer detailsGrade: High School
Subject: Physics
Chapter: Dynamics
If the kinetic energy of an electron is 4.1e-18 j, what is the speed of the electron? (you can use the approximate (nonrelativistic) formula here.)
Final answer:
To find the speed of an electron with a given kinetic energy of 4.1e-18 J, use the non-relativistic kinetic energy formula. The calculation reveals the speed is approximately 2.7 x 10⁶ m/s, validating the use of the classical formula.
Explanation:
If the kinetic energy of an electron is 4.1e-18 J, calculating the speed of the electron involves using the non-relativistic kinetic energy formula, KE = ½mv², where KE is the kinetic energy, m is the mass of the electron (9.11 x [tex]10^-^3^1[/tex] kg), and v is the speed of the electron.
First, rearrange the formula to solve for v, resulting in v = √(2KE/m). Substituting the given kinetic energy and the mass of an electron, we get v = √([tex]2*4.1e^-^1^8[/tex] J / (9.11 x [tex]10^-^3^1[/tex] kg)). Calculating this provides a numerical value for the electron's speed.
After calculating, you'll find that the electron's speed is approximately 2.7 x 10⁶ m/s, which is fast but still less than the speed of light, indicating that using the non-relativistic formula is justified in this scenario.