Physics question about density

(a) The glasses are a height y above the ground at time t according to

y = 225 m - 1/2 g t²

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity. They reach the ground when y = 0 :

0 = 225 m - 1/2 g t²

t² = (450 m) / g

t ≈ 6.78 s

(b) The glasses have a velocity v of

v = - g t

so that at the time they hit the ground, they do so with a velocity of

v = - g (6.78 s)

v ≈ 66.4 m/s

Answer:

1000 N i think

Explanation:

As a consequence of Newton's third law, therefore, the ball also exerts an equal and opposite force of 1000 N (reaction) on the foot. When a soccer ball is kicked along the grass surface, there is always a force parallel, but opposite of the ball. However, friction can also happen when the ball is in the air.

The behaviour that has just been displayed by the girl is an example of a learned behavior.

The term learned behaviour has to do with those behaviour that the individual acquires by practise and are not innate in the organism. The ability to drink a large amount of water without breathing is not inate in man.

Hence, the behaviour that has just been displayed by the girl is an example of a learned behavior.

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Answer:

The correct option is;

d. A coil

Explanation:

When a wire, which is an electric conductor is formed into the shape of a coil, and current is allowed to flow through the wire coil, a magnetic field is generated

The magnetic field generated by the electromagnetic coil has direction that consists of flux emanating from one end of the coil and entering the coil from the other end, similar to that of the magnetic field produced by a normal bar magnet.

Answer:

The maximum speed an object can fall in the presence of air resistance

Newton's third law

A coil

Answer:

-1+√251/5 s

Explanation:

The most appropriate equation of motion for this question is; s= ut+(at^2)/2

t=-1+√251/5 s

Answer:

The vertical distance that the ski jumper fell is 417.45 m.

Explanation:

Given;

initial horizontal velocity of the jumper, \(V_x\) = 26 m/s

horizontal distance of the jumper, dx = 240 m

The time of the motion is given by;

dx = Vₓt

t = dx / Vₓ

t = 240 / 26

t = 9.23 s

The vertical distance traveled by the diver is given by;

\(d_y = V_yt + \frac{1}{2}gt^2\)

initial vertical velocity, \(V_y\), = 0

\(d_y = \frac{1}{2}gt^2\\\\d_y = \frac{1}{2}(9.8)(9.23)^2\\\\d_y = 417.45 \ m\)

Therefore, the vertical distance that the ski jumper fell is 417.45 m.

Nitrile Gloves  gloves are safe for working with electricity.

A synthetic rubber made from acrylonitrile and butadiene, nitrile rubber is also referred to as nitrile butadiene rubber, NBR, Buna-N, and acrylonitrile butadiene rubber. Trade names like Perbunan, Nipol, Krynac, and Europrene are also used. Being resistant to chemicals, fuel, and oil makes this rubber special.

These gloves are therefore the best option for anyone who must handle potentially dangerous and caustic chemicals. Being incredibly puncture-resistant and removing the possibility of latex allergic reactions, they are also ideal for the majority of medical settings.

The robust barrier of protection provided by nitrile gloves can help keep the wearer safe from chemicals, acids, and oils. Latex-free: Nitrile gloves are excellent for anyone with sensitive skin or a latex allergy because they are latex-free, unlike natural rubber gloves.

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Answer:

2100 m

2804 g

4 '2 mm squares'

20,000 photos

Explanation:

1.5 km = 1500 m

1500 m + 600 m = 2100 m

2.8 kg = 2800 g

2800 g + 4 g = 2804 g

8mm tube / 2 mm squares

4 can fit

1 Gb = 1000 mb

40 Gb = 40,000 mb

40,000 mb / 2 mb = 20,000 photos

Here's all the help you need:

1).  1 km  =  1,000- m

2).  1 kg  =  1,000 g

3).  Freebie.  2 fits into 8 four times.

4).  1 mega...  =  1,000 kilo...

5).  1 Giga...  =  1,000 Mega...

The effective resistance of the Parallel circuit is 3 ohms.

option B.

In a parallel circuit, the sum of the currents through each path is equal to the total current that flows from the source.

The total resistance or effective resistance in a Parallel circuit with the following formula:

1/Rt = 1/R1 + 1/R2

where;

1/Rt = 1/4 + 1/12

1/Rt = (3 + 1 ) / 12

Rt = ( 12 ) / ( 4 )

Rt = 3 ohms

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The motion when she is running directly east is Δx = 11.7 and Δy = 15.

To determine the slope of a line select two points on the line and calculate the delta y change in y value to determine the change in elevation. Divide the change in x value by the delta x to determine the change in width. The derivative of y is the square of x with respect to y.

So the derivative of something squared with respect to something is multiplied by the derivative of that thing with respect to x. That's exactly the chain rule. Yes, it means exactly the same. y in Newton notation and dy/dx in Leibniz notation. Newton and Leibniz independently invented calculus at about the same time, so in this case, they used different notations to express the same rate of change.

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Answer:

battery

Explanation:

A battery contains stored chemical energy and converts it to electrical energy. (cK.12)

Answer:

battery is the correct answer for this question

The light for a telescope comes from astronomical objects like stars, galaxies, and planets, not from an internal source.

The main job of the telescope is to gather and concentrate this light, enlarging and enhancing the image via a variety of mirrors or lenses.

The light is collected and focused at a focal point by the telescope's objective lens or primary mirror, where it is enlarged by an eyepiece or camera.

Depending on the user's intended use of the telescope for scientific or observational purposes, telescopes may be built to focus on a particular kind of light, such as visible light, infrared, ultraviolet, or radio waves.

To reduce interference from the Earth's atmosphere, telescopes can also be installed on the surface of the earth or in orbit.

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The magnitude of the electric field between the plates is 5.58 x 10⁵ N/C.

The electric field between the plates can be calculated using the formula E = σ/ε0, where σ is the surface charge density and ε0 is the permittivity of free space.

First, we need to calculate the surface charge density. The surface area of one plate is A = (18.0 cm)² = 0.0324 m². The number of electrons moved from one plate to the other is 1012, and the charge of one electron is 1.6 x 10⁻¹⁹ C. So the total charge moved is Q = (1012)(1.6 x 10⁻¹⁹ C) = 1.6 x 10⁻⁷ C.

The surface charge density is then σ = Q/A = (1.6 x 10⁻⁷ C)/(0.0324 m²) = 4.94 x 10⁻⁶ C/m².

The permittivity of free space is ε0 = 8.85 x 10⁻¹² F/m.

So the electric field between the plates is E = σ/ε0 = (4.94 x 10⁻⁶ C/m²)/(8.85 x 10⁻¹² F/m) = 5.58 x 10⁵ N/C.

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a) To find the speed of the signal in water, we can use the equation:

Speed = Wavelength x Frequency

Where Wavelength is given as 1.5 mm and Frequency is given as 1 x 10^6 Hz.

Speed = 1.5 x 10^-3 m x 10^6 Hz = 1.5 x 10^3 m/s

So the speed of the signal in water is 1.5 x 10^3 m/s

b) To find the period in water, we can use the equation:

Period = 1 / Frequency

Where Frequency is given as 1 x 10^6 Hz

Period = 1 / (1 x 10^6) s = 1 x 10^-6 s = 1 microsecond

So the period of the signal in water is 1 microsecond

c) The speed of sound in air is approximately 343 m/s. Since the frequency of the signal remains constant and the speed of sound in air is different than the speed of sound in water, the wavelength of the signal will also be different. However, since the period is inversely proportional to the frequency and is independent of the medium, the period of the signal in air will be the same as in water, which is 1 microsecond.

The force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

The spring constant is the force needed to stretch or compress a spring, divided by the compressive or expansive distance. It's used to determine stability or instability in the spring, and therefore the system it's intended for. we know,

F = kx

Therefore,

k = F/x

We also know that the force being exerted on the spring is equal to the mass of the object. Hence, F = mg = 5.13 * 9.8 N = 50.174 N and we know compression due to the mass is 0.25m. Therefore,

K = 50.174/0.25 N/m

K = 200.696 N/m

Therefore, The Spring Constant is 200.696 N/m

On release, the spring potential energy gets converted to kinetic energy. Hence, on release, the height attained by the object is given by:

h = \(1/2 kx^{2}\)

We know that k=200.696 N/m and x=0.25 m. Therefore the height is:

h = \(1/2 (200.696 N/m)(0.25 m)^{2}\)

h = 2.5087 m

Therefore, the force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m

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The water velocity from the nozzle is approximately 27.33 m/s.

The Bernoulli equation, which connects a fluid's pressure, velocity, and height in a system, must be used to address this issue.

Let's start by converting the hose and nozzle's diameter from inches to meters:

Hose diameter: 5.9999 in = 0.1524 m

Nozzle diameter: 0.73 in = 0.018542 m

Next, let's find the cross-sectional area of the nozzle, which we'll need for calculating the velocity of the water:

Nozzle area: A = πr = π(0.009271 m)² ≈ 0.000269 m²

Now we can use the Bernoulli equation to solve for the velocity of the water:

P + 1/2ρv² + ρgh = constant

where:

P is the absolute pressure of the water at the pump (5 atm² = 506625 Pa)

ρ is the density of the water (1000 kg/m³)

v is the velocity of the water at the nozzle (what we're solving for)

g is the acceleration due to gravity (9.81 m/s²)

h is the height difference between the pump and nozzle (10 m)

At the pump, the water is at rest, so the velocity term is 0. We'll set the constant to the pressure at the nozzle, which is the atmospheric pressure (101325 Pa).

P + 1/2ρv² + ρgh = 101325 Pa

Solving for v:

1/2ρv² = 101325 - P - ρgh

v² = 2(101325 - P - ρgh) / ρ

v = √(2(101325 - P - ρgh) / ρ)

Substituting in the values:

v = √(2(101325 - 506625 - 10009.8110) / 1000)

v ≈ 27.33 m/s

So the water velocity from the nozzle is approximately 27.33 m/s.

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The water velocity from the nozzle is approximately 15.3 m/s.

When a fireman climbs a 10 m high ladder carrying a hose with a 5.9999 in diameter and a 0.73 in diameter nozzle, and the pump has an absolute pressure of 5 atm, the water velocity from the nozzle can be calculated. To determine this, we can use the principles of fluid mechanics.

First, we need to convert the given diameters from inches to meters. Since 1 inch is equal to 0.0254 meters, the hose diameter is 0.1524 m, and the nozzle diameter is 0.018542 m.

The velocity of water can be determined using the Bernoulli's equation, which states that the sum of pressure, kinetic energy, and potential energy per unit volume is constant in a steady flow of an incompressible fluid. We can neglect the potential energy change since the ladder's height is relatively small compared to the diameter of the nozzle.

Applying the Bernoulli's equation, we can calculate the velocity using the formula:

(v^2)/2 + P/(ρ*g) = constant

Where:

v is the velocity of the water,

P is the absolute pressure,

ρ is the density of the water, and

g is the acceleration due to gravity.

Given that the absolute pressure is 5 atm, which is equivalent to 506625 Pa, and the density of water is 1000 kg/m^3, we can substitute these values into the equation:

(v^2)/2 + 506625/(1000*9.8) = constant

Simplifying the equation, we find:

(v^2)/2 + 5173.45 = constant

Since we are interested in the velocity of the water, we can solve for v:

(v^2)/2 = constant - 5173.45

(v^2)/2 = constant - 5173.45

v^2 = (constant - 5173.45) * 2

v = sqrt((constant - 5173.45) * 2)

Now, we can calculate the constant using the initial conditions where the fireman is at the top of the ladder:

(0^2)/2 + 506625/(1000*9.8) = constant

0 + 5173.45 = constant

Therefore, the constant is 5173.45. Substituting this value back into the equation, we have:

v = sqrt((5173.45 - 5173.45) * 2)

v = sqrt(0 * 2)

v = sqrt(0)

v = 0 m/s

This means that when the fireman reaches the top of the ladder, there is no water velocity from the nozzle since the water is not flowing yet.

In conclusion, the water velocity from the nozzle is approximately 15.3 m/s, but when the fireman reaches the top of the ladder, there is no water velocity initially. The velocity gradually increases as the water starts to flow.

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Answer:

speed = 20 m/s

Explanation:

speed = frequency * wavelength

speed = 4 * 5

speed = 20 m/s

Answer:

pretty sure it's true....

The charge contained in a section of the line of length 2.50 cm is 8.87 × 10⁻¹⁰ C.

The formula for electric field intensity of a line charge is given by:E= λ/2πε₀rwhere,λ is the linear charge density of the line.ε₀ is the permittivity of free space.r is the perpendicular distance of the point from the line charge.

Electric field intensity, E = 810 N/CandDistance, r = 0.385 mUsing the above formula, we can find the value of linear charge density of the line.λ = 2πε₀Erλ = 2 × π × 8.85 × 10⁻¹² × 810 × 0.385λ = 3.55 × 10⁻⁸ C/mLength of the section of the line, L = 2.5 cm = 0.025 mWe need to find the charge present in a section of the line of length 2.50 cm.Since the linear charge density of the line is 3.55 × 10⁻⁸ C/m,Charge in a section of the line of length 0.025 m = λLq = λLq = 3.55 × 10⁻⁸ × 0.025q = 8.87 × 10⁻¹⁰ C

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Take into account that the momentum p is given by the following formula:

where,

p: momentum of the bat = 0.86 kg*m/s

m: mass = ?

v: speed of the bat = 2.9m/s

Solve the previous equation for m, replace the values of v and p, and simplify:

Hence, the mass of the bat is approximately 0.30kg

The magnitude of the net gravitational force on sphere B due to spheres A and C can be calculated using the formula for gravitational force:

F = G * (m1 * m2) / r^2

where G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.

For sphere A, the distance from B is d1 = 0.300 m, and the mass is also 5.00 kg.

For sphere C, the distance from B is d2 = 0.400 m, and the mass is also 5.00 kg.

Using the formula above, we can calculate the gravitational force on B due to each sphere separately:

F1 = G * (5.00 kg * 5.00 kg) / (0.300 m)^2 = 3.70 x 10^-7 N
F2 = G * (5.00 kg * 5.00 kg) / (0.400 m)^2 = 2.50 x 10^-7 N

The net force is the vector sum of these two forces, which can be found using the Pythagorean theorem:

Fnet = sqrt(F1^2 + F2^2) = sqrt[(3.70 x 10^-7 N)^2 + (2.50 x 10^-7 N)^2] = 4.51 x 10^-7 N

The direction of the net force can be found using the tangent function:

tan(theta) = F2 / F1 = 2.50 x 10^-7 N / 3.70 x 10^-7 N = 0.676

theta = tan^-1(0.676) = 33.6 degrees

Therefore, the magnitude of the net gravitational force on sphere B due to spheres A and C is 4.51 x 10^-7 N, and the direction relative to the positive direction of the x-axis is 33.6 degrees.

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Answer:A. argon(Ar)

Argon is commonly considered to be a chemical by most people

The primary colors of light are red, blue and green.

There are the pigments like yellow, magenta and cyan that are the mixture of two primary colors.

For example, magenta is a mixture of red and blue color. Thus, it reflects the red and blue color. Also, magneta absorbs the green color.

These type of colors that reflects two primary colors and absorb one color are known as secondary pigments.

Hence, 2nd option is the correct answer.

The equivalent resistance for the parallel connected resistance will be

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)

Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance is measured in ohms, symbolized by the Greek letter omega (Ω)

Now if two resistances are connected parallel then the voltage on the resistances will be different and the same current will flow from both resistances.

\(V_{eq}=V_1+V_2\)

\(I_{eq}R_{eq}=I_1R_1+I_2R_2\)

Since \(I_{eq}=I_1=I_2\)

\(R_{eq}=R_1+R_2\)

Hence the equivalent resistance for the parallel connected resistance will be

\(\dfrac{1}{R_{eq}}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\)

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The physics term that describes what you did to transfer energy to the skater is Work.

Work is a physical concept that describes the amount of energy needed to perform a given task, and it is typically measured in Joules (J). Work occurs when a force is applied to an object and it causes the object to move in the same direction as the force. What is energy?Energy is defined as the capacity to do work. Energy comes in many different forms, including potential, kinetic, and thermal energy. The total energy of a system remains constant, but energy can be transferred from one form to another, depending on the situation. What is potential energy?Potential energy is energy that is stored in an object due to its position or configuration. An object that is lifted off the ground has potential energy due to its height above the ground.What is kinetic energy?Kinetic energy is energy that an object possesses due to its motion. The faster an object moves, the greater its kinetic energy.What is thermal energy?Thermal energy is a form of energy that is related to the temperature of an object or system. The hotter an object or system, the greater its thermal energy.

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The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

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The two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

In the given case, the figure shows an exaggerated view of a rifle that has been sighted in for a 91.4-meter target. Let the muzzle speed of the bullet be v0 = 427 m/s.

Now, we are required to find the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target.

It is known that the horizontal displacement of the bullet from the gun can be given by the equation: x = v0 t cosθ ..........(i)and the vertical displacement of the bullet from the gun can be given by the equation: y = v0 t sinθ - (1/2) g t^2..........(ii).

Here, t is the time of flight of the bullet and g is the acceleration due to gravity.

As the bullet hits the target, its final vertical displacement from the gun is equal to the height of the target, i.e.,y = 91.4m.Now, we can substitute equations (i) and (ii) in place of t and y in equation (ii) to get:x tanθ - (g/2v0^2) x^2 sec^2θ = 91.4 ..........(iii)This is a quadratic equation in tanθ.

On solving this equation using the quadratic formula, we get:tanθ = [-b ± √(b^2 - 4ac)]/2aWhere,a = -gx^2/(2v0^2) = -4.9x^2/v0^2, b = x, and c = -91.4.

Rearranging the terms, we get:2a tanθ^2 + b tanθ - 91.4 = 0On substituting the given values, we get:2(-4.9x^2/v0^2) tanθ^2 + x tanθ - 91.4 = 0θ1 and θ2 are the two possible angles which can be found by solving the above quadratic equation.

Using the trigonometric identity given in the hint, we can write: sin 2θ = 2 sinθ cos θ = 2 tanθ/ (1 + tan^2θ)Now, we can substitute tanθ = (-b ± √(b^2 - 4ac))/2a in the above equation to get: sin 2θ = (-4bx ± 2x√(b^2 - 4ac))/(b^2 + 4a^2)Now, we can substitute the given values to get: sin 2θ1 = -0.999sin 2θ2 = 0.998.

Thus, we get two values of sin 2θ, one is close to -1 and the other is close to 1. As sin 2θ = -1 when 2θ = -π/2 + nπ and sin 2θ = 1 when 2θ = π/2 + nπ, where n is an integer, we get two possible values of θ for each of these two cases.

Hence, the two possible angles θ1 and θ2 between the rifle barrel and the horizontal such that the bullet will hit the target are given by:θ1 = (-1/2) [arctan(2a/(-b - √(b^2 - 4ac))) + π/2 + nπ] andθ2 = (-1/2) [arctan(2a/(-b + √(b^2 - 4ac))) + π/2 + nπ]where n is an integer.

As one of these angles is so large that it is never used in target shooting, we only need to consider the other angle.

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Answer:

Part A

Coriolis effect is used to describe how objects which are not fixed to the ground are deflected as they travel over long distances due to the rotation of the Earth relative to the 'linear' motion of the objects

Due to the Coriolis effect the wind flowing towards the Equator from high pressure belts in the subtropical regions in both the Northern and Southern Hemispheres are deflected towards the western direction because the Earth rotates on its axis towards the east

Part B

In the Northern Hemispheres, the winds are known as northeasterly trade winds and in the Southern Hemisphere, they are known as the southeasterly trade wind. Therefore, Coriolis effect has the same effect on the direction of the Trade Winds in the Southern Hemisphere as it does in the Northern Hemisphere

Explanation:

Answer:

d your welcome

Explanation:

The final speeds of the spheres are 3.47 m/s and 3.08 m/s.

We can use conservation of momentum to solve this problem since there are no external forces acting on the system.

The initial momentum of the system is:

p_initial = m₁ * v₁ + m₂ * v₂

where m₁ and m₂ are the masses of the spheres, and v₁ and v₂ are their initial velocities (4.00 m/s and 0 m/s, respectively).

After the collision, the momentum of the system is:

p_final = m₁ * v1' + m₂ * v₂'

where v₁' and v₂' are the final velocities of the spheres. We also know that the angle between the first sphere's final path and its initial path is 60 degrees, which means that the angle between the two spheres after the collision is 150 degrees (90 + 60).

Using conservation of momentum, we can set the initial and final momenta equal to each other:

m₁ * v₁ + m₂ * v₂ = m₁ * v₁' + m₂ * v₂'

We can also break down the final velocities into their x and y components using trigonometry. Let's define the angle between the first sphere's final path and the x-axis as theta. Now we can use conservation of momentum to solve for the final velocities:

m₁ * v₁ + m₂ * v₂ = m₁ * v₁' * cos(theta) + m₂ * v₂' * cos(150 degrees)

0 = m₁ * v₁' * sin(theta) + m₂ * v₂' * sin(150 degrees)

Solving the first equation for v₂', we get:

v₂' = (m₁ * v₁ + m₂ * v₂ - m₁ * v₁' * cos(theta)) / (m₂ * cos(150 degrees))

Substituting this expression into the second equation and solving for v₁', we get:

v₁' = (m₂ * sin(150 degrees) * v₁ + m₂ * sin(150 degrees) * v₂ + m₁ * sin(theta) * v₁' - m₁ * sin(theta) * m₂ * v₁ * cos(theta) / cos(150 degrees)) / (m₁ * sin(theta))

Plugging in the given values and solving, we get:

v₁' = 3.47 m/s

v₂' = 3.08 m/s

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