Two piloted satellites approach one another at a relative speed of 0.25 m/s, intending to dock. The
first has a mass of 4.00 × 103 kg, and the second a mass of 7.50 × 103 kg. If the two satellites collide
elastically rather than dock, what is their final relative velocity?

Answer:

Explanation:

Form must follow function, otherwise the design of a structure is a failure.  For example, the function (purpose) of a bridge is to provide a means of crossing an obstacle, such as a body of water, a valley, another road, etc.  The form of the bridge must serve the purpose of providing safe and reliable passage of pedestrians, vehicles, trains, etc.  A most basic form of a bridge is a beam design: simple, efficient, cost-effective, functional.  If budget and public sentiment allow, additions to the design can be incorporated to make the bridge more aesthetically pleasing, but such additions do not add to the basic function.  

The centripetal force of the object is determined as 48 N.

Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle. It is the force that keeps the object moving in a circle, rather than continuing in a straight line.

The centripetal force required to keep an object moving in a circle is given by the formula:

F = (mv²)/r

where:

Substituting the given values, we get:

F = (12 kg)(8.0 m/s)² / 16 m

F = 48 N

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The complete question is below:

A 12 kg object has a velocity of 8.0 m/s and is moving in a circle of a radius 16 m. calculate the centripetal force of the object

Answer:

M 1 L 1 T-2

Explanation:

Answer:

Impervious surfaces

Explanation:

Impervious surfaces are paved or hardened surfaces that do not allow water to pass through. Roads, rooftops, sidewalks, pools, patios and parking lots are all impervious surfaces.

Velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.

Rate and direction of an object's movement is known as velocity.

Let velocity of airplane A with respect to the ground be "vA" and  velocity of airplane B with respect to the ground be "vB". Velocity of A relative to B, denoted as vAB, is calculated:

vBx = vB cos(60°) = 200 km/h x cos(60°) = 100 km/h

vBy = vB sin(60°) = 200 km/h x sin(60°) = 173.2 km/h

Direction of vBy is north-west.

Velocity of A with respect to the ground is given as 300 km/h north.

vAB = vA - vB

vABx = vAx - vBx = 300 km/h - 100 km/h = 200 km/h

vABy = vAy - vBy = 300 km/h - 173.2 km/h = 126.8 km/h

So, the velocity of airplane A relative to B is 200 km/h east and 126.8 km/h north-west.

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Given :-

To find:-

Answer :-

Here we are given that the sunspots temperature is 4360K , and considering it as a black body we need to find out the wavelength of its maximum intensity.

So here we can use Wein's displacement Law according to which;

[tex]\qquad\: \underset{\rm\small Wein's \ displacement \ law }{\underbrace{\underline{\underline{ \green{ \quad\quad\lambda_{max}= b/T \quad\quad}}}}} \\[/tex]

where ,

Now on substituting the respective values, we have;

[tex]\implies \lambda_{max}= \dfrac{2.89\times 10^{-3}m\ K}{4360K}\\[/tex]

[tex]\implies \lambda_{max}= 0.0006628 \times 10^{-3}\ m\\[/tex]

[tex]\implies \lambda_{max}=0.000663 \times 10^{-3}\ m\\[/tex]

[tex]\implies\underline{\underline{\green{ \lambda_{max}= 663 \times 10^{-9} m = 663\ nm }}} \\[/tex]

Hence the maximum wavelength is 663 nm .

and we are done!

The radius of curvature for the turn is 0.10 m. The time required for a bee to execute a 90 degree turn is 0.56 seconds.

Bumblebees are skilled aerialists and can fly with confidence around and through the leaves and stems of plants. They navigate obstacle-filled tracks by maintaining a reasonably constant centripetal acceleration of 4.0 m/s2 while turning right and left in level flight at a constant speed of 0.40 m/s.

The centripetal acceleration of a body moving in a circular path can be expressed as a = v^2 / r, where a is the centripetal acceleration, v is the speed of the body, and r is the radius of curvature.

Given that the bumblebees maintain a constant centripetal acceleration of 4.0 m/s^2 while turning, and their speed is 0.40 m/s, we can calculate the radius of curvature as:

r = v^2 / a = 0.40^2 / 4.0 = 0.04 m = 0.10 m (rounded to two significant figures)

To find the time required for a bee to execute a 90 degree turn, we need to know the distance it travels during the turn. Since the turn is a quarter of a circle, the distance traveled is a quarter of the circumference of the circle with a radius of 0.10 m, which is:

d = (πr)/2 = (3.14 x 0.10)/2 = 0.157 m

The time required to travel this distance at a constant speed of 0.40 m/s is:

t = d/v = 0.157 / 0.40 = 0.3925 s = 0.56 s (rounded to two significant figures)

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Answer:

Explanation:

To find out how many years the United States could run on the energy released by a 10²³ J solar flare, we need to divide the energy of the solar flare by the energy consumed by the United States in one year:

Number of years = Energy of solar flare / Energy consumed by the United States per year

Number of years = 10²³ J / 2.5 x 10¹⁹ J/year

Number of years = 4 x 10³ years

Therefore, the United States could run for approximately 4,000 years on the energy released by a 10²³ J solar flare.

The formula for calculating the cross-sectional area of a cylinder is:

A = πr^2

The intersection of a cylinder is the area of a shape found if the cylinder is cut perpendicular to its length. This will be a circle for a cylinder. The cross-sectional area of a cylinder is calculated as A = πr^2, where A is the cross-sectional area, is a mathematical constant approximately equal to 3.14, and r is the radius of the cylinder.

This formula computes the volume of a sphere of radius r, which is the cylinder's cross-sectional area. We can calculate various cylinder properties such as thickness, surface area, and so on by knowing the cross-sectional area.

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The formula for calculating the cross-sectional area of a cylinder is Area = πr^2 where 'r' is the radius of the cylinder. An example is provided where the radius is 5 units, yielding a cross-sectional area of 78.5 square units.

The cross-sectional area of a cylinder can be calculated using the formula for the area of a circle, because a cross-section of a cylinder is a circle. The formula is Area = πr^2, where 'r' is the radius of the cross-section.

For example, if you have a cylinder with a radius of 5 units, you would calculate the cross-sectional area as follows:

So, the cross-sectional area of this cylinder is 78.5 square units.

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Kirchhoff's current law (KCL) can be written at each node using nodal analysis, and the voltages can be expressed in terms of the node voltages using Ohm's law.

The most chosen reference node in the nodal analysis is. a node that is connected to by the most elements. a node that has the greatest amount of voltage sources linked to it, or. a symmetry node.

An order template data node that references another data node is known as a reference node. The structure and data typing of the reference data node match those of the node it is referencing.

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Therefore, the net electric force acting on particle 3 due to particle 1 and particle 2 is -1.38 x 10⁻⁵ N (repulsive).

Charge is a fundamental property of matter that describes how strongly an object interacts with electromagnetic fields, such as electric and magnetic fields. There are two types of charge: positive and negative. Like charges repel each other, while opposite charges attract each other. The SI unit of charge is the Coulomb (C). Charge is conserved, meaning that the total amount of charge in a closed system remains constant over time. Charge can be transferred between objects through various mechanisms, such as friction, conduction, and induction. The movement of charged particles, such as electrons or ions, is the basis for electric current and many other electrical phenomena. The study of electric charge and its effects is known as electrostatics.

Here,

To find the net electric force acting on particle 3 due to particle 1 and particle 2, we can use Coulomb's law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them:

F = k * (q1 * q3 / r13²) + k * (q2 * q3 / r23²)

where F is the net electric force on particle 3, k is Coulomb's constant (9.0 x 10⁹ N m²/C²), q1, q2, and q3 are the charges of particles 1, 2, and 3, respectively, r13 and r23 are the distances between particles 1 and 3, and particles 2 and 3, respectively.

To find the distances between the particles, we can use the fact that the triangle is equilateral and has sides of length 3.5 cm. By using trigonometry, we can find that the distances are:

r13 = r23 = 3.5 cm

Substituting the values into the equation, we get:

F = (9.0 x 10⁹ N m²/C²) * [(-8.3 nC) * (8.0 nC) / (0.035 m)² + (-16.6 nC) * (8.0 nC) / (0.035 m)²]

F = -1.38 x 10⁻⁵ N (repulsive)

The direction of this force can be found by considering the angles between the sides of the equilateral triangle and using vector addition. The direction is 120 degrees counterclockwise from the positive x-axis.

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(a) The pitch factor of a three-phase winding is given by Kp = cos(π/6m), where m is the number of slots per pole per phase. Here, m = 48 slots/(4 poles x 3 phases) = 4 slots/pole/phase. Therefore, Kp = cos(π/6 x 4) = cos(π/2) = 0.

(b) The distribution factor of a double-layer winding is given by Kd = sin(π/2p), where p is the number of poles. Here, p = 4, so Kd = sin(π/8) = 0.3827.

(c) The frequency of the voltage produced in the stator winding is given by f = (P/2) × (N/60), where P is the number of poles and N is the speed of rotation in rpm. Here, P = 4 and N = 1800 rpm, so f = (4/2) × (1800/60) = 60 Hz.

(d) The resulting phase voltage of this stator can be calculated using the formula Vφ = 4.44 × f × Φ × Z × K, where Φ is the flux per pole, Z is the total number of conductors in series per phase, and K is the product of the pitch factor and the distribution factor. For this winding, Z = 10 turns/coil x 2 coils/slot x 48 slots/3 phases = 160 conductors/phase, and K = 0 x 0.3827 = 0.

Therefore, Vφ = 4.44 × 60 × 0.054 × 160 × 0 = 0 V.

Since this is a three-phase winding, the resulting terminal voltage will be the line-to-line voltage, which is √3 times the phase voltage. Therefore, the resulting terminal voltage of this stator is 3 × Vφ = 3 × 0 = 0 V.

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Answer:

The objective of this study is to determine the duration of time it takes for an object with an initial velocity of 15 m.s-1 to reach its peak height and descend back to its starting point when launched straight upwards, such as when throwing a ball straight up into the air. The study takes into account the effects of gravity, air resistance and Newton's Laws of Motion.

For the purpose of this study, a mathematical investigation is undertaken, taking into consideration the initial velocity (vi = 15 m.s-1) and the gravitational acceleration (g = 9.81 m.s-2). The equation for the Time of Flight (T) is derived by using kinematic equations, as followed:

T = 2vi/g

Where T is the time of flight and vi is the initial velocity of the object.

In this case, the Time of Flight is equal to T = 2∙ 15m/s / 9.81 m/s2 = 3.03 s.

Therefore, when the ball is released into the air the ball was be in the air for 3.03 seconds before descending back to its starting point.

Friction, in this case, does not need to be included in the equations because it's negligible. However, to accurately determine the time the ball reaches its peak, additional equations should be used by considering the forces acting on the object, being drag, air resistance, and gravity

According to the question the caboose travels 7 m after the brakes are applied.

Caboose is a term used to describe the last car in a freight train. It is typically designed to house a crew of railroad personnel, such as a conductor, a flagman, and a brakeman. The purpose of the caboose is to provide a safe place for the crew to observe the train and to signal any errors or problems to the engineer. The caboose also serves as a living and working space for the crew, providing a bed, cooking facilities, and a desk. The signalman in the caboose communicates with the engineer by means of a lamp or radio. The caboose also serves as a weight to help slow the train when necessary.

The work done (350,000 J) is equal to the force applied (70,000 N) multiplied by the distance traveled (x). Therefore, x = 350,000 J / 70,000 N = 5 m. Since the caboose has to travel a distance of 7 m to come to a complete stop, the answer is D. 7 m.

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Answer:

Explanation:

When the free magnet is pushed toward the magnet that is taped down, it will be attracted to it and will move towards it.

The distance between the magnets when the free magnet first starts to be pulled will depend on the strength of the magnets and the orientation of their poles. Use the ruler to measure the distance between the magnets when the free magnet starts to be pulled.

When the magnets are positioned so that their north poles are facing each other, they will begin to repel each other when they are brought close enough. Measure the distance at which the magnets begin to repel each other using the ruler.

The table below shows the positions of the free magnet and the magnet that is taped down, as well as a description of what happens when the free magnet is released.

Position                   Description                                    Diagram

Position 1 The free magnet is placed directly above the magnet that is taped down. When released, the free magnet will stick to the taped down magnet with opposite poles attracting. N-S

Position 2 The free magnet is placed beside the taped down magnet with opposite poles facing each other. When released, the free magnet will move towards the taped down magnet and stick to it. N-S

Position 3 The free magnet is placed beside the taped down magnet with like poles facing each other. When released, the free magnet will move away from the taped down magnet due to repulsion. N-N or S-S

Position 4 The free magnet is placed directly beside the taped down magnet with like poles facing each other. When released, the free magnet will move away from the taped down magnet due to repulsion. N-N or S-S

5-12. Follow the steps to prepare and conduct the experiment using the pieces of tape.

a. Based on the observations in Steps 1-3, it can be concluded that magnetic force is present between two magnets with opposite poles attracting and like poles repelling each other. The strength of the force depends on the distance between the magnets and the orientation of their poles.

b. Part 1 of the Procedure and Data section provided evidence that magnetic fields exist because the magnets were able to exert a force on each other without direct contact. This suggests that there is an invisible force field surrounding the magnet that can interact with other magnetic objects.

c. To determine the size of the magnetic field around the magnet that is taped down, the experiment could be modified by placing the free magnet at different distances from the taped down magnet and measuring the strength of the force between them. This would allow for a better understanding of how the magnetic field changes with distance from the magnet.

d. In Part 2 of the Procedure and Data section, the pieces of tape affected each other due to the presence of electric fields. When the second piece of tape was brought close to the first, it caused a change in the electric field, which in turn caused a change in the behavior of the first piece of tape. Depending on the orientation of the electric fields, the pieces of tape could attract, repel, or have no effect on each other.

e. The experiment allowed evidence to be gathered that electric fields exist by observing the behavior of the pieces of tape when they were brought close to each other. The presence of a change in the behavior of the tape when the electric fields were affected suggests that there is an invisible force field surrounding the tape that can interact with other electrically charged objects.

The experiment demonstrates the principles of magnetism and electrostatics. By moving magnets or charged objects closer or further apart, the extent of the respective fields can be measured.

This experiment demonstrates the invisible forces of magnetism and electrostatics. In steps 1 to 3, the magnets attract each other when their opposite poles (north and south) face each other, and they repel when similar poles (north and north, or south and south) face each other. This distance at which attraction or repulsion starts represents the extent of the magnetic field. In steps 4 to 12, the experiment uses tape to illustrate electrostatic forces. When tape is peeled from a surface, it becomes statically charged. Two pieces of tape that have the same charge will repel each other while different charges attract. The distance at which this occurs represents the extent of the electric field. To measure the size of a magnetic field, you could use a device called a magnetometer or you could move a magnet towards a stationary magnet and measure the distance at which the moving magnet begins to move. These procedures provide evidence of the existence of invisible magnetic fields and electric fields.

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From the nodal analysis, the value of V1 = -3V and the value of I1 = 2A. Voltage, current, and resistance-related versions of Ohm's law exist in three different forms.

A super-node is a concept that can be utilized to solve a circuit in circuit theory. This is accomplished by treating a voltage source on a wire as a point source voltage in comparison to other point voltages present at different nodes in the circuit, relative to a ground node given a charge of zero or negative.

In a network of data communication, a node is a point of intersection or connection. These devices are all referred to as nodes in a networked environment where every device is reachable. Depending on the kind of network it relates to, each node has a different definition.

Applying nodal analysis,

[tex]3+\frac{V1}{3} +\frac{V1}{3} +\frac{V1+2}{1} =0[/tex]

[tex]3+\frac{V1}{3} +\frac{V1}{3} +V1+2=0[/tex]

[tex]\frac{V1+V1+3V1}{3} =-5[/tex]

[tex]\frac{5V1}{3} =-5[/tex]

[tex]V1=-3V[/tex]

Applying again nodal analysis,

[tex]I1+\frac{V1}{3} +\frac{V1+2}{1} =0[/tex]

[tex]I1+\frac{-3}{3} +\frac{-3+2}{1} =0[/tex]

[tex]I1=2A[/tex]

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Answer: The answer is C i believe

Answer:

Tell me why you cried, and why you lied to me

Tell me why you cried, and why you lied to me

Well I gave you everything I had

But you left me sitting on my own

Did you have to treat me, oh, so bad

All I do is hang my head and moan

Tell me why you cried, and why

Explanation:

Answer:

If the wavelength is 2.5 meters, each node will be half a wavelength apart from each other. Therefore, each node will be 1.25 meters apart.

Explanation:

The distance between nodes of a standing wave is equal to half the wavelength of the wave. This is because nodes are points along the wave where there is zero amplitude or displacement, and they occur at fixed intervals that are determined by the wavelength of the wave. Therefore, the distance between nodes is directly proportional to the wavelength of the wave.

Answer: 0.5J

Explanation:

We can use the formula for the potential energy stored in a spring:

U = (1/2) k x^2

where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

Since we want to compress the spring, x will be negative, and we need to find the potential energy change between the uncompressed length and a compression of 10 cm:

U = (1/2) k (0.1 m)^2 - (1/2) k (0 m)^2

U = (1/2) (100 N/m) (0.1 m)^2 - (1/2) (100 N/m) (0 m)^2

U = 0.5 J

So the work required to compress the spring from its uncompressed length to x = 10 cm is 0.5 J.

The amount of work required by the spring to compress it from its uncompressed length (x = 0) to x = 10 cm is 0.5 J.

In order to compress a spring, the following formula must be used:

Work is equal to (1/2)*k*(xf² - xi²)

where:

xi = starting position = 0 m

xf = final position = 10 cm = 0.1 m k = spring constant = 100 N/m

By entering these values, we obtain:

W = (1/2) * 100 N/m * (0.1 m)² = 0.5 J

Hence, it takes 0.5 J of work to compress the spring from its uncompressed length to x = 10 cm (joules).

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The distance traveled by the rock at 3.5seconds is 392ft.

Distance moved by a body can be calculated by using the following formula:

Speed = distance/time

Acceleration = speed/time

According to this question, gravity causes a rock to accelerate downwards at a rate of 32 ft/sec/sec. The speed can be calculated as follows:

Speed = 32ftsec-² × 3.5sec

Speed = 112ft/sec

Distance moved = 112ft/sec × 3.5sec

Distance = 392ft

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Answer:

from - from the mouth .............

Answer:

i) Total charge of the

system

= 2 x 10 -7 + (-2 x 10 -7)

= zero P

(ii)

P =q x 2i

P= 2 x 10-7 x 20 x 10-2

P = 4 x 10-8 cm

Direction of Dipole moment – Along negative z-axis.

Explanation:

Answer:

Explanation:

The size of each push determines the magnitude of the force applied on the car. The force of friction on the car is the resistance force that opposes the motion of the car and it depends on the nature of the surface in contact and the weight of the car. The force of friction is equal and opposite to the force applied on the car, as per Newton's third law of motion.

If the magnitude of the net force on the car is greater than the force of friction, the car will accelerate in the direction of the net force. If the magnitude of the net force is equal to the force of friction, the car will move at a constant velocity. If the magnitude of the net force is less than the force of friction, the car will decelerate and eventually stop.

Therefore, the size of each push needs to be greater than the force of friction on the car to accelerate it. If the size of each push is equal to the force of friction, the car will not accelerate, and if the size of each push is less than the force of friction, the car will decelerate.

Answer & Explanation:

we need to calculate how much the ball drops due to the effect of gravity over the 60.5 ft distance from the pitcher's mound to home plate. We can use the formula:

d = 1/2 x g x t^2

where:

d is the distance the ball drops (in ft)

g is the acceleration due to gravity (32.2 ft/s^2)

t is the time it takes for the ball to travel 60.5 ft at a horizontal speed of 102.5 mi/h (which we need to convert to ft/s)

Converting the horizontal speed from miles per hour to feet per second:

102.5 mi/h = 102.5 x 5280 ft / 3600 s = 150.7 ft/s

Now we can find the time it takes for the ball to travel 60.5 ft:

t = d / v

t = 60.5 ft / 150.7 ft/s

t = 0.401 seconds

Finally, we can use the time to calculate how far the ball drops vertically:

d = 1/2 x g x t^2

d = 1/2 x 32.2 ft/s^2 x (0.401 s)^2

d = 0.517 ft

Therefore, the ball drops vertically by approximately 0.517 ft (or 6.2 inches) by the time it reaches home plate, assuming it is thrown horizontally at 102.5 mi/h.

If a baseball is thrown horizontally at a speed of 102.5 mph, it would fall approximately 2.605 feet vertically by time it reaches the home plate 60.5 feet away.

The subject of this problem belongs to the area of projectile motion. First, we need to know the time it takes for the ball to reach the home plate. Given that the distance to the home plate is 60.5 feet and the ball is thrown at 102.5 mph (which is approximately 150 feet per second when converted), the time can be calculated using the formula

time = distance/speed. This gives us approximately 0.403 seconds.

Next, we use the equation for displacement in the vertical direction under the influence of gravity, h = 0.5gt^2, where g is the acceleration due to gravity (32.2 ft/s^2), and t is time. Plugging in the known values, we get

h = 0.5 * 32.2 * (0.403^2) = 2.605 feet.

Therefore, if a baseball were thrown horizontally at a speed of 102.5 mph, it would drop approximately 2.605 feet vertically by the time it reached the home plate, 60.5 feet away.

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The most likely reason for Nathaniel needing fewer calories than his dad, even though they exercise about the same amount, is his age.

Age plays a significant role in determining person's daily calorie requirements. As people age, their body composition and metabolism change, and they tend to lose muscle mass and gain fat mass, which leads to decrease in their basal metabolic rate (BMR).

BMR is the amount of energy the body needs to carry out its essential functions while at rest. Therefore, even if Nathaniel and his dad have same activity level, Nathaniel's lower BMR due to his age would result in him needing fewer calories than his dad to maintain his weight. Other factors such as gender, activity level, and hunger may also contribute to differences in calorie requirements, but age is the most significant factor in this case.

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Answer:

17. A

18. C

Explanation:

np:) and have a wonderful day

Answer:

motion force

Explanation:

If the catapult throws them then the rocks would be in motions