You are designing a thin transparent reflective coating for the front surface of a sheet of glass. The index of refraction of the glass is 1.52, and when it is in use the coated glass has air on both sides. Because the coating is expensive, you want to use a layer that has the minimum thickness possible, which you determine to be 104 nmnm. Part A What should the index of refraction of the coating be if it must cancel 500-nmnm light that hits the coated surface at normal incidence

The speed of the truck just before braking is 23.24 m/s.

The speed of the truck before braking is calculated by applying the third kinematic equation as shown below.

v² = u² - 2as

where;

When the truck stops, the final velocity = 0

0 = u² - 2as

u²  = 2as

u = √2as

u = √ ( 2 x 6 x 45 )

u = 23.24 m/s

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The  spring constant is 400 N/m. For the given question.

What is spring constant ?

The spring constant (k) is a physical property of a spring, which represents the stiffness of the spring. It is defined as the force required to stretch or compress a spring by a certain amount (x) divided by that amount of deformation:

k = F/x

where F is the applied force and x is the displacement or deformation of the spring from its equilibrium position. The spring constant has units of force per unit of length, such as newtons per meter (N/m) in the SI system of units. A higher spring constant means that more force is required to deform the spring by the same amount, and the spring is considered to be stiffer. Conversely, a lower spring constant means that less force is required to deform the spring by the same amount, and the spring is considered to be more flexible.

We can use the conservation of energy to find the spring constant.

Initially, the box has kinetic energy given by:

K₁= (1/2)mv₁²

= (1/2)(4.0 kg)(3.0 m/s)²

= 18 J

At maximum compression, all of the kinetic energy is stored as potential energy in the spring. The potential energy stored in a spring is given by:

U = (1/2)kx²

where k is the spring constant and x is the displacement from the equilibrium position. In this case, x is the compression of the spring, which is 0.30 m.

So, the potential energy stored in the spring is:

U = (1/2)kx²

= (1/2)k(0.30 m)²

= 0.045k J

Since energy is conserved, we can equate the initial kinetic energy to the potential energy stored in the spring:

K₁= U

18 J = 0.045k J

k = 400 N/m

Therefore, the spring constant is 400 N/m.

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Answer:

b) 1.67×10^7 m/s

Explanation:

The solution is attached in the attachment section

The motion of electron is oscillatory about the center of the ring. The speed of the electron when it reaches the center of the ring is equal to  1.23 × 10⁷ m/s.

The force between the two electric point charges is called electrostatic force. An electrostatic force can be attractive or repulsive depending upon the n the polarity of the charges.

The electron will be attracted toward the center of the ring where the net force is zero. But the electron has some kinetic energy and due to inertia it crosses the center, but on the other side, it is further attracted towards the center of the ring.

Given ,the radius of the ring, r = 0.15cm

The total charge on the ring, q = 20 × 10⁻⁹ C

The distance of the electron from the center of the ring, x = 0.3m

Consider that the charge 'e' on the electron,

Force due to the charge ring on the electron is:

\(F_e = \frac{kq_1q_2x}{(r^2+x^2)^{3/2}}\)

\(F_e = \frac{kqex}{(r^2+x^2)^{3/2}}\)

\(F_e =\frac{8.99\times 10^9\times 20\times 10^{-9}\times 1.6 \times 10^{-19}\times 0.3}{(0.15^2+0.3^2)^{3/2}}\)

\(F_e =22.89\times 10^{-17} N\)

The electron accelerates due to electrostatic force,

F = ma

22.89×10⁻¹⁷ = 9.1 × 10⁻³¹ × a

a = 2.52 × 10¹⁴ m/s²

The speed of the electron to the center of the ring will be, from the equation of motion:

v² - u² = 2ax

v² = 2× 2.52× 10¹⁴ × 0.3

v = 1.23 × 10⁷ m/s

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Answer:

1.2703 km

Explanation:

The speed can be calculated using the formula;

Speed (m/s) = distance (m) ÷ time (s)

Based on the information in this question, it took 3.7 seconds for a sound with speed of 1236 km/h to reach John. The distance will be:

Distance = speed × time

However, we need to convert the time in seconds (s) to hour (hr).

1 second = 0.000277778 hour

3.7 seconds = 0.00102778 hours.

Hence,

distance = 1236 × 0.00102778

Distance = 1.2703 km

Answer:

0.1 m/s

Explanation:

Please see attached photo for explanation.

Mass of 1st cart (m₁) = 500 g

Initial velocity of 1st cart (u₁) = 0.25 m/s

Mass of 2nd cart (m₂) = 750 g

Initial velocity of 2nd cart (u₂) = 0 m/s

Velocity (v) after collision =.?

m₁u₁ + m₂u₂ = v(m₁ + m₂)

(500 × 0.25) + (750 × 0) = v(500 + 750)

125 + 0 = v(1250)

125 = 1250v

Divide both side by 1250

v = 125 / 1250

v = 0.1 m/s

Thus, the two cart will move with a velocity of 0.1 m/s after collision.

The velocity of the cart will be 0.1 m/sec.Velocity is the rate of change of displacement. Its unit is m/sec.

According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.

The given data in the problem is;

(m₁)  is the mass of  cart 1 = 500 g

(u₁)  is the initial velocity of  cart  1= 0.25 m/s

(m₂) is the mass of 2nd cart = 750 g

(u₂) is the initial velocity of 2nd cart  = 0 m/s

(v)  is the velocity after collision =.?

According to the law of conservation of momentum;

Momentum before collision =Momentum after collision

\(\rm m_1u_1 + m_2u_2 = v(m_1 + m_2)\\\\(500 \times 0.25) + (750 \times 0) = v \times (500 + 750) \\\\ 125 + 0 = v \times (1250) \times 125 \\\\ \rm v= \frac{125}{1250} \\\\ \rm v== 0.1 m/sec\)

Hence the velocity of the cart will be 0.1 m/sec.

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Answer:

We are given the length, the mass and the density of the cylinder. First let us calculate for the volume by dividing the mass by the density.

volume = mass /density

where mass = 2.17 kg = 2170 g, therefore:

volume = 2170 g / (2.33 g/cm^3)

volume = 931.33 cm^3

We know that the volume of a cylinder has the formula:

volume = π r^2 h

since h = 16.8 cm, therefore calculating for radius:

931.33 cm^3 = π r^2 (16.8 cm)

r^2 = 17.646 cm^2

r = 4.2 cm

Hence the diameter (d) is:

d = 2 r

d = 8.4 cm

Explanation:

The diameter of the cylindrical rod is approximately 0.382 cm.

To find the diameter of the cylindrical rod, we can use the formula for the volume of a cylinder and then solve for the diameter.

The formula for the volume of a cylinder is:

V = π\(r^{2}\)h,

where V is the volume, r is the radius, and h is the height (or length) of the cylinder.

In this case, we know the length of the cylinder (h) is 16.8 cm. We need to find the radius (r) in order to calculate the diameter.

The mass of the cylinder can be related to its volume and density using the formula:

m = ρV,

where m is the mass, ρ is the density, and V is the volume.

Rearranging this formula, we can solve for V:

V = m / ρ.

Now we have two equations:

V = π\(r^{2}\)h,

V = m / ρ.

Setting these two equations equal to each other, we can solve for r:

π\(r^{2}\)h = m / ρ.

Substituting the given values:

π\(r^{2}\) * 16.8 cm = 2.17 kg / (2.33 g/\(cm^3\)).

Let's solve this equation for r:

\(r^{2}\) = (2.17 kg / (2.33 g/\(cm^3\))) / (π * 16.8 cm).

\(r^{2}\)  ≈ 0.036775 \(cm^2\).

Taking the square root of both sides:

r ≈ 0.191 cm.

Finally, we can find the diameter (d) by multiplying the radius by 2:

d ≈ 2 * 0.191 cm.

d ≈ 0.382 cm.

Therefore, the diameter of the cylindrical rod is approximately 0.382 cm.

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An electric iron is marked 120 volts and 500 Watts. The units consumed by it in using it for 24 hours can be calculated using the formula:Power (in watts) = Voltage (in volts) x Current (in amperes)P = V x I

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Answer:

Below

Explanation:

EPE = 1/2 k x^2      for a spring  where x = amount of compression or stretch

 450 = 1/2 (100) x^2

  450 ( 2)/100 = x^2 = 9     so x = 3 m

The theorem showing that △ ABC ≅ △ def is Density functional theorem.

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Answer:

750m/s

Explanation:

v = fλ = (1500 Hz)(0.5 m) = 750m/s

Answer:

0.5 m and 1500 Hz divided by 750 m/s equals 750 m/s.

Explanation:

Brainliest pls!

The potential energy is at the maximum when you reach the top of your jump on a trampoline. The correct answer is option B.

Potential Energy is the type of energy an object possesses by virtue of its position relative to others, stresses within itself, electric charge, and other factors. Potential energy exists in various forms, including gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy.

This type of energy can be converted into another type of energies. Examples, a charged battery has potential energy and it can be used as electrical potential energy. Petrol, diesel and and gas have chemical potential energy and be used as kinetic energy.

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Answer:

This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.

The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.

The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).

The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:

R(n) = √(X² + Y²)

Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.

However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:

<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2

<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2

Because <X²> = <Y²>, we can write:

<R²> = <X²> + <Y²> = n A²

So, the root mean square distance (the square root of the mean square displacement) after n steps is:

R(n) = √(<R²>) = √(n) * A

Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.

Answer:

12.0 V

Explanation:

Data :

Potential difference due to a single charge (+Q), E = 3.0 V

The Electric potential for the system of charges is given as:

\(E=\frac{1}{4\pi \epsilon_o}[\Sigma\frac{Q}{r}]\)

for single charge, E = 3.0 V = \(\frac{1}{4\pi \epsilon_o}[\frac{Q}{r}]\)  ->eq(1)

And for 4 charges:

\(E=\frac{1}{4\pi \epsilon_o}[4\frac{Q}{r}]\) -eq(2)

from eq(1) and (2) we have

E = 4 × 3.0 V = 12 V

Answer:

Time cause it's so long ago I was just

When the floor started to heat because of the warmer weather, the wooden floor started to dilate due to the increase in thermal energy, increasing its area. Since there wasn't space for it to expand, the floor started to buckle.

Then, trimming the edges of the floor was the solution, because this way the floor has space to expand due to dilation.

The statement that correctly states this information is found in option B.

Answer:

Liquids

Explanation:

Diffusion occurs fastest in liquids.

Older adults have greater freedom to pursue interests, to use time, to think, and to reflect is not positive aspects of aging.

Early adulthood is the beginning of a long, ongoing process of natural change called aging. Many body processes start to gradually deteriorate in the early middle years. At no particular age do people become old or elderly. Old age has traditionally been defined as commencing at age 65.

Oxidative stress, glycation, telomere shortening, adverse responses, mutations, and protein aggregation are a few of the factors that contribute to aging.

Positive aspects of aging except older adults have greater freedom to pursue interests, to use time, to think, and to reflect.

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Answer:

A.) They will repel, moving in opposite directions at the same speed.

Explanation:

The correct option is - A.) They will repel, moving in opposite directions at the same speed.

As because the two balloons have identical charge and moving towards each other , so they repel each other (as we know like charges repel each other)

Option A is correct. (A.) They will repel, moving in opposite directions at the same speed. Because the megnitude and nature of the charge are same.

The force of attraction between two charges, according to Coulomb's law, is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Charges that are similar repel each other, whereas charges that are diametrically opposed attract each other.

They will repel, moving in opposite directions at the same speed. Because the megnitude and nature of the charge are same.

Hence option A is correct. (A.) They will repel, moving in opposite directions at the same speed.

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Answer:

V = a t      velocity after time t

t = 33.1 / 9.80 = 3.38 sec   (time ball had been falling)

S = 1/2 a t^2 = 55.9 m

So the ball had been falling  for 7 * 8 = 56 m  

The child was 7 floors from the top

Since he was on the eight floor the floors below him were

7 * 8 + 12 = 68 m     total floors below child

68 + 56 = 124 m      total height of building

Total floors in building = 7 + 7 + 1 = 15 floors

PE at top = KE at bottom

KE = m g h = .125 * 9.80 * 124 = 152 Joules

Speed and velocity are related to an object's kinetic energy, which is the energy associated with its motion.

Kinetic energy is the energy that an object has due to its motion. It is a form of energy that is associated with the motion of an object, and is calculated by multiplying the mass of the object by the square of its velocity. Kinetic energy is one of the most fundamental forms of energy, and is found in everything from the movement of atoms and molecules to the motion of planets and stars. Kinetic energy is also the energy that is associated with everyday objects, such as a ball that is thrown or a car that is moving. Kinetic energy can be converted into other forms of energy, such as heat or electricity, and can also be used to do work, such as powering a car or a machine. Kinetic energy is a crucial part of the natural world, and is necessary for many of the processes that occur in nature.

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Answer:

100

Explanation:

Use equation p=mv

p=(50kg)(2m/s)= 100

Answer:

a)40 meters

b)2 m/s

c)2 m/s

d)0 m/s

e)45 degrees northeast

Explanation:

a) The displacement from C to A is the distance directly across the river, which is 40 meters.

b) The speed of the boat as seen by people standing at A is the magnitude of the boat's velocity vector, which is equal to the displacement divided by the time taken:

Speed = displacement / time = 40 m / 20 s = 2 m/s.

c) Let v be the speed of the water in the river. The boat is moving at right angles to the flow of the river, so the water exerts a perpendicular force on the boat. The time taken for the boat to travel from A to C is 20 seconds, during which time the boat will have been carried downstream by the river by a distance equal to v times the time taken.

Distance carried downstream = v × time = v × 20 m.

Since the boat landed at C, which is directly across the river from A, the distance it traveled horizontally is 40 meters. Therefore:

40 m = (boat speed) × (time taken) = (boat speed) × 20 s.

Hence, the speed of the boat is:

Boat speed = 40 m / 20 s = 2 m/s.

So, we have two equations:

Distance carried downstream = v × 20 m

Boat speed = 2 m/s

From the first equation, we get:

v × 20 m = 40 m

Therefore, the speed of the water in the river is:

v = 40 m / 20 m = 2 m/s.

d) The speed of the boat as seen by a fish drifting with the river is the difference between the speed of the boat and the speed of the water in the river:

Boat speed - Water speed = 2 m/s - 2 m/s = 0 m/s.

So, the speed of the boat as seen by a fish drifting with the river is zero.

e) The boat should head in a direction that makes its velocity vector point directly from A to B. Since A and B are directly opposite each other, this means the velocity vector should be perpendicular to the line connecting A and B.

We know the boat's velocity vector has a magnitude of 2 m/s and is at right angles to the velocity vector of the water in the river, which has a magnitude of 2 m/s. So, we can draw a vector diagram with the velocity vector of the boat pointing straight up and the velocity vector of the water pointing straight to the right. The vector connecting the tail of the water velocity vector to the head of the boat velocity vector will then point directly from A to B.

The angle between the boat's velocity vector and the line connecting A and B can be found using trigonometry. Let θ be this angle. Then:

tan(θ) = (boat speed) / (water speed) = 2 m/s / 2 m/s = 1.

Taking the inverse tangent of both sides gives:

θ = tan^(-1)(1) = 45°.

So, the boat should head in a direction 45 degrees to the right of straight up, or northeast.

The minimum horizontal velocity the diver must have to clear the rocks, given that it extend outward for 16 m is 4.82 m/s

We'll begin by obtaining the time taken for the diver to reach the ground. Details below

h = ½gt²

54 = ½ × 9.8 × t²

54 = 4.9 × t²

Divide both side by 4.9

t² = 54 / 4.9

Take the square root of both side

t = √(54 / 4.9)

t = 3.32 s

Now, we shall determine the horizontal velocity the diver must have. Detail below:

s = ut

16 = u × 3.32

Divide both sides by 3.32

u = 16 / 3.32

u = 4.82 m/s

Thus, the horizontal velocity is 4.82 m/s

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Answer:

Use Fc centripetal force as positive and W the weight as negative

N = m v^2 / R + m g

v^2 = (N - m g) R / m

v^2 = (995 - 57 * 9.8) 42.7 / 57 = 327 m^2/s^2

v = 18.1 m/s

Note: N - m g is the net force producing the centripetal force

a) The value of t u = 140/t`b.

b) The y position of the cannonball at the time t is  55.5 mc.

c) The initial speed of the projectile is 52.4 m/s.

Given that a cannonball is fired horizontally from the top of a cliff. The cannon is at height H = 55.5 m above ground level, and the ball is fired with initial horizontal speed u. The projectile lands at a distance D = 140 m from the cliff. Assume that the cannon is fired at time t = 0 and that the cannonball hits the ground at time t.Now,We have to find the value of t, y position of the cannonball at the time t and the initial speed of the projectile.

a. To find the value of t:Here, we have to use the formula of distance

i.e.,S = ut + (1/2)gt², Where S = 140 m, u = u and g = 9.8 m/s².Hence,140 = u×t ………..(1)We know that, time taken by the cannonball to hit the ground can be calculated as,`(2H)/g`

Since the height of the cannon from the ground is 55.5m, the total height of the cannonball from the ground is

(2H) = 2 × 55.5

= 111 m`2H/g

= 111/9.8`

= 11.32653 s

From equation (1),u×t = 140u = 140/t

Therefore, `u = 140/t`b.

b)To find the y position of the cannonball at the time t:

Here, we have to use the formula of height i.e.,y = u×t – (1/2)gt²,

Where, y = height of the cannonball at time t, u = 140/t, t = time taken by the cannonball to hit the ground and g = 9.8 m/s².

We have already calculated the time taken by the cannonball to hit the ground in the previous step.`

y = 140 - (1/2) × 9.8 × t²`

On substituting the value of t as `t = 11.32653`,

we get,y = 140 - (1/2) × 9.8 × (11.32653)²= 55.5 mc.

c)  To find the initial speed of the projectile:

To calculate the initial speed of the projectile, we need to use the formula of range of projectile

.i.e.,R = u²sin2θ/g

Where R = 140 m, g = 9.8 m/s², θ = 0° (horizontal)

u² = R × g/sin2θ

   = 140 × 9.8/sin0°  

   = 2744m²/s²u  

   = \(\sqrt(2744m^2/s^2)\)

   = 52.4 m/s

Hence, the initial speed of the projectile is 52.4 m/s.

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When an object's mass or velocity are both zero, it can have zero momentum. Given that there is no negative mass, the velocity should be 0, indicating that the object is at rest.

FALSE - Because its velocity is higher than that of the more massive item, a less massive object would have a greater momentum. Mass and velocity are two factors that affect momentum. Both have equal value.

Although two objects of equal mass and speed moving in opposing directions have no net momentum, they do have net kinetic energy.

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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