Gwen is baby-sitting for the Parker family. She takes 3-year old Allison to the
neighborhood park and places her in the seat of the children's swing. Gwen pulls the
1.8-m long chain back to make a 26° angle with the vertical and lets 14-kg Allison
(swing mass included) go. Assuming negligible friction and air resistance, determine
Allison's speed at the lowest point in the trajectory.

If you are running at a constant velocity, you should throw the ball slightly forward with respect to you so that you can catch it yourself. Therefore, option D is correct.

An object is said to be moving at constant velocity when it is moving straight and fast. As a result, the item is not accelerating, which is defined as a change in velocity over time in either direction or speed. In other words, there is no net force acting on an item that is travelling at a constant speed.

If there are no forces acting on an object or if those forces are balanced, the object can have a constant velocity. A car is going with constant velocity, for instance, if it is moving at a constant speed in a straight path on a flat road with no external forces acting on it. Likewise, if a thing is going straight line at a constant speed through a vacuum, with no external forces acting upon it, then it is also moving with constant velocity.

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Answer: The velocity of the truck after the collision is 18.2 m/s.

Explanation:

Step 1: Determine the total momentum of the two vehicles before the collision.

Momentum is equal to mass multiplied by velocity (p = mv). The momentum of the car before the collision was 900 kg x 20 m/s = 18,000 kg m/s. The momentum of the truck before the collision was 1,100 kg x 15 m/s = 16,500 kg m/s. The total momentum of the two vehicles before the collision was 34,500 kg m/s.

Step 2: Determine the total momentum of the two vehicles after the collision.

After the collision, the car moves back 18 m/s so the momentum of the car is now 900 kg x (-18 m/s) = -16,200 kg m/s. The momentum of the truck after the collision is not given, so we will use the letter "v" to represent this. The total momentum of the two vehicles after the collision is then -16,200 kg m/s + (1,100 kg x v).

Step 3: Use the law of conservation of momentum to solve for the velocity of the truck.

The law of conservation of momentum states that the total momentum of two objects before a collision is equal to the total momentum of two objects after the collision. This means that 34,500 kg m/s = -16,200 kg m/s + (1,100 kg x v), or 34,500 kg m/s = -16,200 kg m/s + 1,100v. Since we know all of the values on the right side of the equation, we can solve for v by rearranging the equation. We get v = (34,500 kg m/s + 16,200 kg m/s) / 1,100 kg = 18.2 m/s.

Therefore, the Step 1: Determine the total momentum of the two vehicles before the collision.

Momentum is equal to mass multiplied by velocity (p = mv). The momentum of the car before the collision was 900 kg x 20 m/s = 18,000 kg m/s. The momentum of the truck before the collision was 1,100 kg x 15 m/s = 16,500 kg m/s. The total momentum of the two vehicles before the collision was 34,500 kg m/s.

Step 2: Determine the total momentum of the two vehicles after the collision.

After the collision, the car moves back 18 m/s so the momentum of the car is now 900 kg x (-18 m/s) = -16,200 kg m/s. The momentum of the truck after the collision is not given, so we will use the letter "v" to represent this. The total momentum of the two vehicles after the collision is then -16,200 kg m/s + (1,100 kg x v).

Step 3: Use the law of conservation of momentum to solve for the velocity of the truck.

The law of conservation of momentum states that the total momentum of two objects before a collision is equal to the total momentum of two objects after the collision. This means that 34,500 kg m/s = -16,200 kg m/s + (1,100 kg x v), or 34,500 kg m/s = -16,200 kg m/s + 1,100v. Since we know all of the values on the right side of the equation, we can solve for v by rearranging the equation. We get v = (34,500 kg m/s + 16,200 kg m/s) / 1,100 kg = 18.2 m/s.

Therefore, the velocity of the truck after the collision is 18.2 m/s.

The speed of the car after it has traveled 25.0 m is 3.87 m/s. when the car starts from rest and accelerates at 0.300 m/s2.

A vector quantity is acceleration. We must provide retar-dation—a negative acceleration—to the body in order for it to come to rest. The body's velocity is zero when it comes to a stop. The outcome is that the acceleration is also zero.

Acceleration is a vector quantity. The body needs to experience retar-dation—a negative acceleration—in order to come to rest. When a body comes to a stop, its velocity is zero. As a result, the acceleration is zero as well.

v^2 = u^2 + 2as

v = final velocity

u = initial velocity = zero [start from rest]

a = acceleration = 0.300 m/s2

s = distance = 25.0 m

v^2 = 0 + 2 [0.300] [25.0]

v^2 = 15

v^2 = 3.87 m/s

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Hare can afford to nap if he does not want to lose the race is of 3690 seconds.

A unit rate is a cost for only one of anything. Unit rate is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

D = 1000m

v = 0.27 m/s

t = 1000/0.27

t = 3703.7 sec

Time taken for 100m for hare.

t = 100/15

t = 6.7 sec

Therefore, total time t is

t = 7 + tn + th

3703.7 = 7 + tn + 6.7

tn = 3703.7 - 13.7

tn = 3690 sec

Therefore, hare afford to nap if he does not want to lose the race is 3690 sec.

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The total energy radiated by the Sun each second when emissivity of the Sun is 0.986 is 3.85×10²⁶ W .

The power output of the Sun is given by Stefan's law , i.e

P=σAeT 4

=(5.6696×10⁻⁸ W/m².K⁴ )[4π (6.96×10⁸m)² ]×(0.986)(5800K)⁴

=3.85×10²⁶ W

The total energy radiated by the Sun each second when emissivity of the Sun is 0.986 is 3.85×10²⁶ W .

The radiation radiated from an area A of a black body at absolute temperature T is directly proportional to the fourth power of the temperature, according to Stefan Boltzmann's law.

The total energy emitted or radiated by a black body per unit surface area across all wavelengths and per unit time is inversely related to the black body's thermodynamic temperature to the fourth power.

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The dependence of the rate constant on temperature is expressed by the Arrhenius equation.

The Arrhenius equation is an equation that is used to describe the relationship between the reaction rate of a chemical reaction and the temperature at which the reaction takes place. The equation states that the reaction rate is equal to the frequency factor (A) multiplied by the product of the Boltzmann constant (k) and the temperature (T) raised to the power of the activation energy (E): rate = A * kT^E.

Therefore, The dependence of the rate constant on temperature is expressed by the Arrhenius equation.

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The acceleration due to gravity varies according to the size of the planet.

Here is a list of the acceleration due to gravity (g) on the Moon and on the planets in our Solar System:

Moon:

g = 1.62 m/s^2

Mercury:

g = 3.7 m/s^2

Venus:

g = 8.87 m/s^2

Earth:

g = 9.8 m/s^2

Mars:

g = 3.71 m/s^2

Jupiter:

g = 24.79 m/s^2

Saturn:

g = 10.44 m/s^2

Uranus:

g = 8.87 m/s^2

Neptune:

g = 11.15 m/s^2

It's worth noting that the acceleration due to gravity is affected by the mass and size of a celestial body. Larger and more massive objects have a stronger gravitational pull and therefore a higher acceleration due to gravity.

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The car's weight and mass in kg if cable from a to b must exert a 8500 n horizontal force on the car to hold it in place is 14722N and 1502.24 kg.

Believe or not, weight is the force that the earth Earth is acting on you. The gravitational acceleration which is multiplied to the mass is deduced by using the equation of Newton's law of solemnity similar that one mass is the mass of the earth Earth.

The free body diagram is shown to the right

Applying the equilibrium equation

[tex]\sum F_s = T- Nsin30\degree = 0\\\\\sumF = Ncos30 - mg = 0\\[/tex]

Setting T = 8500N and solving the equation we get,

N = 17000N

mg = 14722 N

So weight = 14722 N

and mass = 14722/g = 14722/9.8 = 1502.24 kg

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The force of friction of the ball is 870.8N.

Friction is the force that resists motion when the surface of one object comes in contact with the surface of another.

Frictional force is the force generated by two surfaces that contact and slide against each other.

Frictional force can be calculated by multiplying the normal force by coefficient of friction as follows:

f = F × µ

Where;

f = 58.4kg × 9.81m/s² × 1.52

f = 870.8N

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The mallet in contact with the ball is 2.4 milliseconds.

The amount of time that the mallet was in contact with the ball can be calculated using the equation for impulse, which is equal to the change in momentum. Force and time combine to create an impulse.. Mathematically, it can be expressed as:

Impulse = Change in Momentum = F * t

Change in momentum is the product of mass and change in velocity.Therefore, the time that the mallet was in contact with the ball can be calculated as follows:

[tex]t = \frac{Impulse }{F }\\ \\= \frac{(0.45 kg * 1.3 m/s) }{ 83 N }\\\\= 2.4 milliseconds[/tex]

Therefore,The mallet in contact with the ball is 2.4 milliseconds.

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the first piece of observational proof that the universe is old. He found that a galaxy appears to be moving away from us faster the further away it is from us, using the greatest telescope available at the time. The universe is therefore evenly expanding in all directions.

We frequently observe bigger fluctuations in the color of the light that distant galaxies release when we measure their radiation. This indicates that they are travelling more quickly than the nearby galaxies.

Speeds that are not faster than 0.05% to 1.0% the speed of light. However, you don't need to gaze very far away—100 million light-years is more than enough—to see the consequences of the expanding Universe.

Therefore, Galaxy W is twice as far as Galaxy X.

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The period of a pendulum is found to be 5.26 seconds if the pendulum string has a length of 7 meters.

A pendulum may be characterized as a body suspended from a fixed point so that it can swing back and forth under the influence of gravity. The time interval of a pendulum's complete back-and-forth movement is constant.

According to the question,

The length of a pendulum string = 7 m.

The period of a pendulum string = ?

The length of a pendulum string is found with the help of the following formula:

        7 = (T/2 × 3.14)² × 9.8

        7 = [tex]\frac{T^2}{4}[/tex] × 9.85 × 9.8.

        28 = [tex]T^2[/tex] × 96.53 = 0.526 = 5.26 seconds.

Therefore, the period of a pendulum is found to be 5.26 seconds if the pendulum string has a length of 7 meters.

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The minimum distance between the driver and the camper when he first sees it so that they do not collide is 16.86 m.

Distance is the physical length between two points. It is a measure of the space between two objects or a point and a line. Distance can be measured in various ways, such as in meters, kilometers, feet, inches, miles, and even light-years. Distance can also refer to the amount of time or effort required to reach a destination.

The minimum distance between the driver and the camper when he first sees it so that they do not collide is calculated using the following formula:
d = vₒt + (1/2)at²
Where d is the distance, vₒ is the initial velocity, t is the reaction time, and a is the deceleration.
Plugging in the given values, we get:
d = 31.3 m/s × 0.39 s + (1/2) × 3.0 m/s² × (0.39 s)²
d = 16.86 m
Therefore, the minimum distance between the driver and the camper when he first sees it so that they do not collide is 16.86 m.

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The electrostatic force exerted on the electron will be in the direction of the electric field, which is from the positive plate to the negative plate. Since the electron is negatively charged, it will be attracted to the positively charged plate, so the force on the electron will be in the direction from the negative plate to the positive plate.

The electrostatic force, also known as the Coulomb force, is the force that exists between electrically charged particles. It is a fundamental force of nature that governs the behavior of charged particles, such as electrons and protons.

The electrostatic force is responsible for many natural phenomena, such as the attraction and repulsion of magnets, the electric shock felt after rubbing a balloon on hair, and the behavior of lightning. It is also used in a wide range of technologies.

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The time period of oscillations of an air bubble formed by an explosion inside water depends on the pressure (P), density (p), and energy due to explosion (E). The relationship between these factors can be established using the principles of fluid mechanics and the equations for pressure, density, and energy.

The pressure of a gas inside a bubble is related to its volume and temperature, and can be described by the Ideal Gas Law:

P = (nRT)/V

where n is the number of moles of gas, R is the gas constant, T is the temperature, and V is the volume of the gas.

The density of a fluid is related to its mass and volume, and can be described by the equation:

p = m/V

where m is the mass of the fluid and V is its volume.

The energy due to the explosion can be described by the equation:

E = (1/2)mv^2 + P_0V_0 - P_fV_f

where m is the mass of the gas, v is its velocity, P_0 and V_0 are its initial pressure and volume, and P_f and V_f are its final pressure and volume.

By combining these equations and using the principles of fluid mechanics, it is possible to establish a relationship between the time period of the oscillations (T), pressure (P), energy due to the explosion (E), and density (p). However, the exact relationship will depend on the specific conditions of the explosion and the fluid in which it occurs.
________________________________________________________

The automobile may slide or skid sideways off the road if the road is covered with ice and the vehicle is being driven at a slower rate of speed than the indicated bank angle.

A vehicle is kept driving in a circular path without sliding by the centripetal force created by the bank angle of a road bend.

This force is produced by the tire-perpendicular normal force of the road, which acts on the tire.

The bank angle is intended to boost the normal force to counteract the centrifugal force that seeks to pull the automobile away from the curve as speed rises.

On an ice road, however, there is a considerable reduction in the coefficient of friction between the tires and the surface, which also affects the normal force.

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The force on the cart by the spring after 2 sec is -906.4 N.

The motion of the cart connected to a spring can be described by the equation:

x = A × [tex]e^-bt/2m}[/tex] × cos(wt - phi)

where:

x is the displacement, A is the amplitude of the motion b is the damping coefficient m is the mass of the cart w is the angular frequency of the motion phi is the phase angle

To find the force on the cart after 2 seconds, we need to find the values of the amplitude, angular frequency, and phase angle. The amplitude can be found from the initial displacement:

A = 2 m

The angular frequency can be found from the frequency of motion:

w = 2πf = 2π(1.8 Hz) ≈ 11.31 rad/s

The phase angle can be found from the initial conditions. At t = 0, the displacement is 2 m and the velocity is 0, so the phase angle is 0. Therefore: phi = 0

Now we can find the displacement of the cart at t = 2 s:

x = A × [tex]e^-bt/2m}[/tex] × cos(wt - phi)

x = 2 ×[tex]e^{-0.1(2)/2(0.5)}[/tex] × cos(11.31(2) - 0)

x ≈ 1.41 m

The force on the cart by the spring can be found using Hooke's Law, which states that the force is proportional to the displacement:

F = -kx

where k is the spring constant. The spring constant can be found from the angular frequency:

w = √(k/m)

k = m × w²

k = 0.5 kg × (11.31 rad/s)²

k ≈ 642.6 N/m

Therefore, the force on the cart at t = 2 s is:

F = -kx

F = -642.6 N/m × 1.41 m

F ≈ -906.4 N

Note that the negative sign indicates that the force is acting in the opposite direction of the displacement (i.e. restoring force).

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The goose will take 8.55 hours to travel 550 km at their average speed of 64.3km/h.

The goose average speed is around 40 mph or 64.3 km/h, but in good weather and wind conditions this speed can go up to 70 mph or 112 km/h

Considering the formula:

x = v.t

were x=space, v=speed and t= time. Clearing the equation, to find the hours of flight:

t = x/v = 550km / 64.3km/h = 8.55 hours

Average speed is a useful concept in many fields, including physics, engineering, and transportation. It can be used to calculate travel times, estimate fuel consumption, and analyze the performance of machines and vehicles. However, it is important to note that average speed does not take into account changes in direction or acceleration, which can affect the overall performance of an object.

Average speed is a measure of how quickly an object moves over a certain distance. It is defined as the total distance traveled divided by the time it takes to travel that distance. The units of average speed are usually expressed as distance per unit time, such as kilometers per hour, miles per hour, or meters per second.

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Katherine Johnson accepted that the meetings were only for men and didn't ask to attend.

Meetings are when two or more people get together to talk about one or more topics, frequently in a formal or business setting, though they can also happen in a variety of other settings. Group decision-making can be done during meetings.

A meeting is a gathering of two or more individuals called for the express purpose of engaging in verbal interaction in order to accomplish a common objective, such as exchanging information or coming to a consensus. Face-to-face meetings can take place virtually through the use of communications technology, such as a telephone conference call, a skped conference call, or a videoconference.

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Statements which are correct are (a) i.e. Telescopes on the ground cannot see the majority of electromagnetic waves. & (d) The Chandra and Spitzer telescopes are all in space.

(a) Most types of electromagnetic waves, such as X-rays and gamma rays, are not visible to ground-based telescopes due to the absorption of these waves by the Earth's atmosphere. Therefore, to detect these types of electromagnetic waves, space-based telescopes are needed.

(d) This statement is correct. The Chandra X-ray Observatory and the Spitzer Space Telescope are both space-based telescopes designed to observe X-rays and infrared radiation, respectively. Since X-rays and infrared radiation are not visible to ground-based telescopes due to the Earth's atmosphere, space-based telescopes are necessary to detect them.

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The correct answer is (d): (1) these elements have become more common as the universe has grown older. (2) these elements should be found in nearly all star systems.

The elements that make up life (such as carbon, nitrogen, oxygen, and iron) are created in stars through nuclear fusion and supernova explosions. As the universe has grown older, more and more stars have been born and died, producing these elements and spreading them throughout the universe. Therefore, these elements have become more common over time.

              Additionally, because these elements are created in stars, they should be found in nearly all star systems. While the exact abundance of these elements may vary depending on the age and type of star, they should be present in some amount in most stars.

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Both at the north pole and one at the equator on the surface of the globe. The centripetal acceleration is greater for the person on the equator.

The centripetal acceleration is the acceleration that is directed towards the center of a circular path. On the surface of the Earth, the rotation of the planet around its axis creates a circular path for any object on its surface. This means that any object on the Earth's surface is subject to a centripetal acceleration due to the Earth's rotation.

The magnitude of the centripetal acceleration:-

a = v²/r

here, v tangential velocity of the object

r radius of circular path.

The tangential velocity is velocity of the object in the direction tangent to the circular path.

The tangential velocity of an object on the surface of the Earth is given by:-

v = ω r

here, ω is angular velocity of the Earth's rotation,

r is radius of the Earth.

The angular velocity is rate at which the Earth rotates around its axis.

Since, the radius of the Earth is largest at the equator, an object at the equator has a larger radius than an object at the North Pole. This means that the tangential velocity of an object on the equator is larger than the tangential velocity of an object at the North Pole. Therefore, the centripetal acceleration of an object on the equator is larger than the centripetal acceleration of an object at the North Pole.

In summary, an object on the Earth's surface experiences a centripetal acceleration due to the Earth's rotation, and the magnitude of this acceleration is determined by the tangential velocity and the radius of the circular path. Since the radius is larger at the equator than at the North Pole, an object on the equator has a larger centripetal acceleration than an object at the North Pole.

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In terms of producing the most energy per unit of carbon dioxide released, natural gas is the best fossil fuel. Because a new crop can be planted after each harvest, biomass is a renewable resource and a low-carbon fuel.

Effects of human activities on the biophysical environment, or environmental challenges, most frequently include. Numerous human activities such as overpopulation, pollution, the burning of fossil fuels, and deforestation have an adverse effect on the physical environment. Climate change, soil erosion, poor air quality, and undrinkable water have all been brought on by changes like these.

There are three main ones that generally have an impact on most of them: the loss of biodiversity, water pollution, ocean acidification, and climate change

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If a voltage of 12 V moves 1.25C of charge between two points then charge must be moved with 15 J in joules of energy.

Here, we need to determine how much energy 12 V expends to transport a charge of 1.25 C between two places.

Voltage, which is defined as the effort or energy necessary to transfer a unit charge between two places, is known to drive electrons in a circuit. It can be calculated mathematically by dividing work/energy by charge.

Thus, we have the equation shown below:

                        [tex]V= \frac{E}{Q}[/tex]

If we rearrange the formula above, we obtain:

                     [tex]E=(V).(Q) (1)[/tex]

Here,

V→ Voltage

E→ Energy

Q→ Charge

Once the values are entered into equation number 1, we will obtain:

                           [tex]E = ( 12 V).( 1.25 C ) = 15 J[/tex]

As a result, we discovered that the amount of energy required to move the charge is 15 J in joules.

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Correct question:

How much energy is expended, in joules, if a voltage of12 V moves 1.25C of charge between two points?

Over the course of a single night, the position of mars in its home constellation do not change dramatically. Correct answer us no.

The position of Mars in its home constellation changes over the course of a single night, but not dramatically. Mars, like all celestial objects, appears to move across the night sky due to the rotation of the Earth.

However, the magnitude of this change in position over the course of a single night is not usually considered to be "dramatic" in astronomical terms. The apparent motion of Mars across the night sky is relatively slow, and its position relative to the surrounding stars may only change by a few degrees over the course of several hours.

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The acceleration between two point on a velocity time graph which has coordinate (10sec,15ms)and (20sec,35ms)​ is 2.5m/s².

This is referred to as the rate at which velocity changes with time, in terms of both speed and direction.

Acceleration = change in velocity/change in time

                          = 35m/s - 15m/s  / 20s - 10s

                            = 25m/s / 10s = 2.5m/s²

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The Earth's angular velocity for its daily rotation on its axis is in the counterclockwise direction (eastward).

The Earth's angular velocity for its daily rotation on its axis is in the eastward direction. From above, this movement would look like the Earth is moving counterclockwise. This means that the Earth rotates from west to east, causing the sun to appear to rise in the east and set in the west. This is also why time zones are arranged with earlier times to the east and later times to the west. The Earth's rotation on its axis is what causes the cycle of day and night.

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