A toy gun shoots marbles by means of a spring. A marble has a mass of .05 kg. The spring used has a spring constant of 30 N/m. When loaded, the marble is displaced an amount of .07 m. The barrel of the gun exerts a slight force of friction on the marble of .075 N as it moves from its starting point a total length of .18 m. If the toy gun is fired horizontally,
a) at what position from the starting point does the marble reach maximum velocity?
b) what is the maximum speed achieved by the marble?
c) how far will it travel if the gun is positioned 2 meters above the ground

After three half-lives, 1/8 (or 0.125) of the parent isotope remains. Thus, 0.125 times the parent atoms. The daughter isotope would be equivalent to the remaining parent isotope, 0.125 times the original number of parent atoms.

After three half-lives, the parent isotope has exponentially decayed, forming the daughter isotope. Each half-life reduces the parent isotope by half and increases the daughter isotope. Three half-lives have passed, reducing the parent isotope to 1/8 of its initial level. The rock sample would have 1/8 of the parent isotope.

The daughter isotope would have accumulated during decay. After three half-lives, the daughter isotope would have reached 3/8 of the parent isotope as each half-life creates one-half of it. After three half-lives, the rock sample would have 1/8 of the parent isotope and 3/8 of the daughter.

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Answer:

Jupiter

Explanation:

Jupiter is the largest planet in our solar system and is about 11 times larger than earth.

The equation that shows the relationship between X₁ and X₂ in the springs is X₁ = 4X₂.

From the complete question, for case I, the two springs stretch up to the distance of X₁. Therefore, f = mg = kx₁.

For case 2, f = mg = kx₂.

Therefore, we'll equate the equations. This will be:

Kx₁ = Kx₂

(K/2)x₁ = (2k)x₂

K(x₁/2) = k(2x₂)

X₁/2 = 2x₂

X1 = 2 × 2x₂

X₁ = 4X₂.

In conclusion, X₁ = 4X₂.

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X₁ = 4X₂ is the equation that shows the connection between X₁ and X₂ in the springs.

The force required to extend or compress a spring by some distance scales linearly with respect to that distance is known as the spring force. Its formula is

F = kx

For case 1;

f=mg=kx₁

For case 2;

f=mg=kx₂

After equating the equation we get;

\(\rm Kx_1 = Kx_2 \\\\ \frac{K}{2}x_1 = (2k)x_2 = k(2x_2) \\\\ \frac{x_1}{2} =2x_2\\\\ x_1 = 4x_2\)

Hence  X₁ = 4X₂ is the equation that shows the connection between X₁ and X₂ in the springs.

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Answer:

the final velocity of the skater after throwing the snowball is 3.17 m/s.

Explanation:

Given;

mass of the ice skater, m₁ = 72 kg

initial velocity of the ice skater, u₁ = 3.1 m/s

mass of the snowball, m₂ = 0.21 kg

initial speed of the snowball, u₂ = 28.0 m/s

Let the final velocity of the skater after throwing the snowball = v

Apply the principle of conservation of linear momentum to determine v;

m₁u₁ + m₂u₂ = v(m₁ + m₂)

72 x 3.1   +  0.21 x 28  = v(72 + 0.21)

229.08 = v(72.21)

v = 229.08 / 72.21

v = 3.17 m/s

Therefore, the final velocity of the skater after throwing the snowball is 3.17 m/s.

The x- and y-components of vector d (magnitude 100 m and at 45 degrees south of east) is x- component \(50 \sqrt{2}$\) and y- component is \(50 \sqrt{2}$\).

A. x component\($=100 \sin 45^{\circ}\)

\(100 \sin \left(45^{\circ}\right)$$\)

Use the following trivial identity: \($\quad \sin \left(45^{\circ}\right)=\frac{\sqrt{2}}{2}$\)

\(=100 \cdot \frac{\sqrt{2}}{2}$$\)

\(100 \cdot \frac{\sqrt{2}}{2}=50 \sqrt{2}$$\)

\($$=50 \sqrt{2}$$\)

y component \($=100 \cos 45^{\circ}\)

\($$100 \cos \left(45^{\circ}\right)$$\)

Use the following trivial identity: \($\quad \cos \left(45^{\circ}\right)=\frac{\sqrt{2}}{2}$\)

\($$=100 \cdot \frac{\sqrt{2}}{2}$$\)

\($$\begin{aligned}&100 \cdot \frac{\sqrt{2}}{2}=50 \sqrt{2} \\&=50 \sqrt{2}\end{aligned}$$\)

A quantity with both magnitude and direction is called a vector. In contrast to a scalar number, a vector quantity also includes a direction component that aids in locating one location in relation to another.

A vector in mathematics is a number that not only defines magnitude but also indicates how an item moves or is positioned in relation to other points or objects. It is sometimes referred to as a spatial vector, geometric vector, or Euclidean vector.

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When an inductor is in a circuit by itself, and the current flows from A to B and is increasing, then Vab is negative.

An inductor is a coil of wire that resists changes in current.

When current is flowing through an inductor, it generates a magnetic field that opposes the change in current direction.

The voltage across an inductor is proportional to the rate of change of the current flowing through it.

The minus sign indicates that the voltage across the inductor is negative.

The voltage across an inductor is opposite to the direction of the current because an inductor generates an electromagnetic field that counteracts changes in current.

When the current flowing through an inductor increases, the magnetic field generated by the inductor opposes the change in current direction by inducing an electromotive force (EMF) that is negative or opposite to the direction of the current.

Therefore, the voltage across the inductor is negative.

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El niño affects the pattern of rainfall over months to seasons by redistributing heat and wind across the Pacific. As the atmosphere above the heated water surface warms, moist air rises and forms rain clouds.

Surface waters in the central and eastern Pacific Ocean become significantly warmer than usual during an El niño event. This shift is inextricably linked to the atmosphere and the winds blowing across the vast Pacific. Easterly trade winds (which blow from the Americas to Asia) weaken and can even turn westward. This allows large amounts of warm water to slosh from the western Pacific toward the Americas. It also reduces the upwelling of cooler, nutrient-rich waters from the deep, slowing or reversing ocean currents along the equator and the west coasts of South and Central America.

The air circulation above the tropical Pacific Ocean responds to this massive redistribution of ocean heat. The eastern Pacific's typically strong high-pressure systems weaken, altering the balance of atmospheric pressure across the eastern, central, and western Pacific. While easterly winds are typically dry and consistent, Pacific westerlies tend to arrive in bursts of warmer, moister air.

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The direction of revolution in the plane of the Solar System was determined by the direction of rotation of the original cloud. The correct option is c.

The solar system was created from a cloud of gas and dust. According to the nebular hypothesis, the sun and planets were formed from a single rotating cloud of dust and gas. The sun was created at the center of the cloud, while the planets were created in orbit around it.

The plane of the solar system's planets is determined by the rotation of the original cloud. The original cloud that formed the solar system was spinning in a specific direction, which determined the direction of revolution in the plane of the solar system. Therefore, the answer is option c. the direction of rotation of the original cloud.

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Option a. When the elevator reaches the 1st floor and comes to a halt, your apparent weight will be less than your true weight.

The apparent weight of an object in an elevator is affected by the force of gravity, the mass of the object, and the acceleration of the elevator. In this case, the elevator is decelerating from the 50th floor to the 1st floor, which means the acceleration is negative. When the elevator reaches the 1st floor and comes to a halt, your apparent weight will be less than your true weight.

To illustrate this concept, consider Newton's Second Law of Motion which states that

Force = Mass x Acceleration (F = ma).

In this case, the force exerted by gravity on the object remains the same (its true weight) but the acceleration changes as the elevator descends. As the acceleration decreases, the apparent weight decreases accordingly.

Therefore, option a is correct.

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The pilot's distance is 2175 miles from her starting position after flying straight for 1.5 hours and making a course correction by flying 2 hours at a 10-degree angle.

To solve this problem, we can break it down into two components: the distance traveled in the original straight path and the distance traveled during the course correction.

1. Distance traveled in the original straight path:

Since the pilot flies for 1 hour and 30 minutes, which is equivalent to 1.5 hours, and her speed is 625 mi/h, we can calculate the distance using the formula:

Distance = Speed × Time

= 625 mi/h × 1.5 h

= 937.5 miles

2. Distance traveled during the course correction:

The pilot flies for 2 hours at a constant speed of 625 mi/h. However, she makes a course correction, which means she is not flying directly away from her starting position. To determine the distance traveled in the new direction, we need to find the horizontal component of the distance traveled.

The horizontal component can be calculated using trigonometry. Since the pilot is heading 10 degrees to the right of her original course, the angle between the original course and the new direction is 10 degrees.

Horizontal Distance = Distance × cosine(angle)

= 625 mi/h × 2 h × cos(10°)

To use the cosine function, we need to convert the angle to radians:

10° × π/180 = 0.1745 radians

Horizontal Distance = 625 mi/h × 2 h × cos(0.1745 radians)

= 625 mi/h × 2 h × 0.9848

= 1237.5 miles

Therefore, the total distance from the starting position is the sum of the distance traveled in the original straight path and the horizontal distance traveled during the course correction:

Total Distance = Distance in original path + Horizontal Distance

= 937.5 miles + 1237.5 miles

= 2175 miles

So, the pilot is 2175 miles from her starting position.

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The reason that explains why such a propeller could not be installed on Manny's airplane is that Manny's airplane is likely not strong enough to withstand the forces caused by flying faster

A propeller is an object with a rotating hub and radiating blades pitched to form a helical spiral that, when rotated, applies linear thrust to a working fluid like water or air.

The propeller's function is to offer a means of propulsion so that the aircraft can move forward through the air. The propeller itself is made up of two or more interconnected blades that are fastened to the engine shaft by a central hub.

A propeller is a device that, when turned, moves you forward through a fluid. In this case, other aircraft have larger, more powerful propellers built into their designs. Manny's aircraft is not strong enough to withstand the forces of faster flight.

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The period of a simple pendulum can be calculated using the equation:

T = 2π√(L/g)

Where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Plugging in the values for a 1.0 m pendulum on Earth, with g = 9.81 m/s^2, we get:

T = 2π√(1.0/9.81) = 2.0064 s

Therefore, the period of a 1.0 m pendulum on Earth is approximately 2.0064 seconds.

On the moon, the acceleration due to gravity is much weaker than on Earth, with g ≈ 1.62 m/s^2. Using the same equation, we can calculate the period of the 1.0 m pendulum on the moon:

T = 2π√(1.0/1.62) = 3.137 s

Therefore, the period of the 1.0 m pendulum on the moon is approximately 3.137 seconds, which is longer than on Earth due to the weaker gravitational force.The period of a pendulum is the time it takes for the pendulum to complete one full swing, from one extreme to the other and back again. The period depends on the length of the pendulum and the acceleration due to gravity. A longer pendulum will have a longer period, while a stronger gravitational force will result in a shorter period. Therefore, the period of a pendulum can be used as a standard unit of time, which can in turn be used to define a standard unit of length. In the case of the 1.0 m pendulum on Earth, its period is approximately 2.0064 seconds, while on the moon, its period is approximately 3.137 seconds, due to the weaker gravitational force.

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Answer:

a. temperature of the substance increases.

Explanation:

Temperature is defined as a measure of the average kinetic energy of a substance, so as one rises, so will the other. They are directly proportional.

As the kinetic energy of the molecules in a substance increases, the temperature of the substance is also increases because kinetic energy and temperature is proportional to each other.

Kinetic energy is directly related to temperature which means if kinetic energy is increased, the temperature of the solution is also increased and vice versa.

So we can conclude that As the kinetic energy of the molecules in a substance increases, the temperature of the substance is also increases because kinetic energy and temperature is proportional to each other.

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The density of gold is 19.38 g/cm³.

We need to know about the density to solve this problem. Density is a unit that measures how dense an object is. Density can be measured by dividing mass by volume. It can be written as

ρ = m / V

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

From the question above, we know that

m = 15.7 grams

V = 0.81 cm³

By substituting the following parameters, we can calculate the density

ρ = m / V

ρ = 15.7 / 0.81

ρ = 19.38 g/cm³

Hence, the density of gold is 19.38 g/cm³.

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Answer:

deceleration? I think because the prefix de means to like not or to slow down

According to  the given statement The force exerted by the string on the object is 2.7 N.

Any item travelling in a circular direction has a tangential velocity, which is its linear speed. On a turntable, a point in the centre moves less distance in a full rotation than a point near the outside edge.

Tangential velocity is determined by dividing the circle's circumference by the time required for one complete rotation: 2*pi*r/t. The formula V = w * r, where w (omega) is the angular velocity of the rotating object and r is the radius of the circle, also relates it to angular velocity.

m = 0.9 kg

r = 3m

v = 3m/s

Force (f) = mv2/r

Now ,putting values

force (f) = \(\frac{0.9 k g \times\left(3 \mathrm{~ms}^{-1}\right)^2}{3 \mathrm{~m}}\)

F = 2.7 N

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Here we are required to determine how the Newtons second law of motion can be algebraically rearranged to solve for acceleration (a).

The correct answer is Choice B: a = F/m

Newton's second law of motion states that the force applied is directly proportional to the rate of change in momentum of the body.

i.e

where (v - u)/t = acceleration, (a)

Therefore, F = ma.

By rearranging; i.e solving for acceleration, (a);

we divide both sides by mass, m

we have;

a = F/m

The algebraic rearrangement to solve for acceleration, (a) is therefore;

a = F/m

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Answer:

Explanation:

speed = distance / time

          = 15 meters / 3 seconds

          = 5 meter / sec.

Answer:5/sec

Explanation:

Answer:

k=1/2mv²

Explanation:

k is the kinetic energy

m is mass

and v is velocity/speed

Answer:

d

Explanation:

To determine the width of a single slit that will produce first-order diffraction minima at an angle of 28° from the central maximum with 710-nm light.

We need to use the following equation: sin(θ) = mλ / w, where θ is the angle of the diffraction minimum, m is the order of the diffraction, λ is the wavelength of the light, and w is the width of the slit. In this case, we know that θ = 28°, m = 1, and λ = 710 nm. We can rearrange the equation to solve for w: w = mλ / sin(θ)
Plugging in the values we have, we get: w = (1)(710 nm) / sin(28°)
Using a calculator, we find that sin(28°) is approximately 0.482. Substituting this value, we get: w = (1)(710 nm) / 0.482
Simplifying, we get: w ≈ 1475 nm
So a single slit with a width of approximately 1475 nm will produce first-order diffraction minima at an angle of 28° from the central maximum with 710-nm light.

To determine the width of the single slit that produces the first-order diffraction minima at an angle of 28° with 710-nm light, we can use the formula for single-slit diffraction: sin(θ) = (mλ) / a
where:
θ = angle from the central maximum (28°)
m = order of the diffraction minima (m = 1 for first-order)
λ = wavelength of the light (710 nm)
a = width of the slit
Rearranging the formula to solve for a, we get: a = (mλ) / sin(θ)
Now, plug in the values: a = (1 * 710 nm) / sin(28°)
a ≈ 1511 nm
The width of the single slit required to produce the first-order diffraction minima at an angle of 28° with 710-nm light is approximately 1511 nm.

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The moment of inertia of the cylinder about the horizontal axis parallel and tangent to the cylinder is 3MR²/2.

The moment of inertia (Icm) of the cylinder about its symmetrical axis is calculated using the formula MR^2/2, where M represents the mass of the cylinder and R represents its radius.

To find the moment of inertia of the cylinder about the axis parallel and tangent to the cylinder, we can use the parallel axis theorem. According to the parallel axis theorem, the moment of inertia about an axis parallel to and at a distance 'd' from the axis passing through the center of mass is given by:

I = Icm + Md^2

In this case, the axis of rotation is parallel and tangent to the cylinder, so the distance 'd' from the axis passing through the center of mass is equal to the radius 'R'. Substituting the values into the equation:

I = Icm + MR^2

I = MR^2/2 + MR^2

I = (1/2 + 1)MR^2

I = (3/2)MR^2

Therefore, the moment of inertia of the cylinder about the given axis is (3/2)MR^2.

The correct answer is (D) 3MR^2/2.

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The terms with their correct definition is matched as follows:

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Answer:

Explanation:

The hand provides Kinetic Energy in moving.

The KE is transformed to Frictional energy

The Frictional Energy can produce heat and light energy.

The sandpaper produces little shreds from the grit of the paper.

The shreds have KE (they move)

\(answer \\ = 50 \: m / s \\ solution \\ distance \: travelled\: by \: bus = 1.5 \: km \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.5 \times 1000 \: m \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1500 \: m \\ time \: = 30 \: seconds \\ speed = \frac{distance}{time} \\ \: \: \: \: \: \: \: \: \: \: = \frac{1500m}{30s } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 50 \: m/s \\ hope \: it \: helps\)

Answer:

C. 50 m/s

Explanation:

Given:

Distance = 1.5 km = 1500 m

Time = 30 sec

Required:

Speed = ?

Formula

Speed = Distance / Time

Solution:

Putting the given in the formula

Speed = 1500/30

Speed = 50 m/s

Answer:Malleability

Explanation:

Answer:

Movement of a magnet relative to a coil produces emfs as shown. The same emfs are produced if the coil is moved relative to the magnet. The greater the speed, the greater the magnitude of the emf, and the emf is zero when there is no motion.

Hope this helps!

Answer:

it should be the second option

Explanation:

I can't really see because the picture is kinda blurry

Answer:

the last option.

Explanation:

A body moving with uniform velocity (the flat line, also called the plateau) and then decelerating. The deceleration is why the velocity decreased.

The concentration of an chemical in an oil spill in ppb is 0.013 ppb (approx).

concentration is the abundance of a constituent divided by the total volume to the  mixture. Several by the  types of mathematical description can be the  distinguished: mass of the  concentration, molar concentration, number and  concentration, and volume concentration.

Calculate the concentration in ppb by multiplying to the  ratio of the mass of solute to  mass of solution by 1 billion or 10 ^9

So here the answer can be calculated by

(10^ 9)(6×10 ^-8)/4600

(Here 0.060 mg = 6 × 10 ^-8 kh)

=  6/460

= 0.013 ppb (approx)

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