analyze what type of collision occurs when a tennis racket hits a ball, as shown in the image, and explain how you know. In addition, predict the motion after the collision.

Answers

Answer 1

The force that is exerted by the racket is greater than the force that is exerted by the ball. Option C

What is momentum?

We have to note that the momentum of the object as we know it is the product of the mass and the velocity of the body. The principle of the conservation of the linear momentum states that the momentum before collision is equal to the momentum after collision.

We can see that the masses of the racket and the ball are not the same and we know hat the object that has the greater mass would surely exert more force as we can see from the image that has been attached to the question that we have in this case here. The collision here is an elastic Collison as is clear from the image.

The racket would then be able to exerted a force  that is exerted by the ball.

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Analyze What Type Of Collision Occurs When A Tennis Racket Hits A Ball, As Shown In The Image, And Explain

Related Questions

A student measures the mass and volume of a sample of aluminum at room temperature, and calculates the density of al to be 2. 85 grams per cubic centimeter. Based on table s, what is the percent error for the student's calculated density of al?.

Answers

The percent error for the student's calculated density of Al during the experiment is 5,56%

The accepted value of the density of aluminum is 2.7 g/cm3.

To calculate the percent error of the student's calculated density of aluminum, one must use the equation:

Percent Error = [Accepted Value - Measured Value] / Accepted Value × 100.

In this case, the percent error is

[2.7 - 2.85]/2.7 ×100 = -5.56%.

This means that the student's measured value was 5.56% lower than the accepted value. This indicates that the student's measurement was slightly lower than the accepted value, but still within an acceptable margin of error

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the most active phase of a thunderstorm is called the ________ phase.

Answers

Answer:

mature stage

Explanation:

This is the stage where.percipitation falls and a downdraft occurs it's the most active be stage hence thunder, lighting and hail

occur

What evidence do you see that newton's third law applies to electrostatic forces?.

Answers

The evidence that newton's third law applies to electrostatic forces is given by Coulomb's law.

According to Coulomb's law, if we take two charges Q1 and Q2 and set them r distance apart from one another, we can state: [tex](\frac{KQ_{1}Q_{2} }{r^{2} } )[/tex]The electrostatic force on [tex]Q_{1}[/tex] by [tex]Q_{2\\}[/tex] is equal to the electrostatic force on [tex]Q_{2}[/tex] by [tex]Q_{1} \\[/tex] And in accordance with Newton's third rule, If object A pulls on object B, then object B pulls in the opposite direction on object A. This demonstrates that the third law of motion of Newton applies to electrostatic force.a) The electric force is an attractive force if the charges of the particles are different or similar, for example, if one particle is positive and the other is negative. (Different charges pull toward one another.

     b). The electric force is a repulsive force if the particles or both charges are positively or negatively charged. Charges oppose one another (like forces).

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The evidence observed from Newton's third law is that the electrostatic force of attraction exerted by two different charges will be equal in magnitude by acting opposite direction.

Newton's third law states that action and reaction are equal and opposite.

For different charges, say a positive charge (+ Q) and negative charge (-Q), the force of attraction exerted by both charges is equal and opposite.

   let the positive charge, +Q = Q₁

   let the negative charge, -Q = Q₂

From Coulomb's law, the force of attraction the two charges will exert on each other is equal and can be calculated as follows;

Thus, the evidence observed from Newton's third law is that the electrostatic force of attraction exerted by two different charges will be equal in magnitude by acting opposite direction.

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Which free the body diagram

Answers

Free body motion with force and friction describes in Newton's second law

Newton's second law.

When a body is in motion with a force and friction, the motion of the body is described by Newton's second law, which states that the acceleration of an object is dependent on the net force applied to it and the mass of the object.

This means that the motion of the body is determined by the sum of all forces acting on it.

This includes both the force applied to the body, as well as the friction forces opposing it. In order for the body to remain in motion, the force applied must be greater than the friction forces acting against it.

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A group of people are pushing a stalled car with a mass of 700kg. If they push with a net force of 200 Newtons for 8 seconds, what is the cars final velocity

Answers

A 700 kg car that has stalled is being pushed by a group of people. The final velocity of the car will be 2.28 seconds if they push with a net force of 200 Newtons for 8 seconds.

What does a change in momentum mean?

The change in momentum (Δp ) is defined as the change in the product of an object's mass and velocity. A force is required to change the momentum of an object. The momentum of the item may change due to the applied force, as well as its direction.

Why is an impulse a change in momentum?

Any moving object can have momentum because momentum is defined as mass in motion. The impulse of an item is equal to its change in momentum. Impulse is defined as a force multiplied by a time period. Instead of being the same as momentum, impulse is the change in momentum of an object.

Impulse = Impulsive force x Impact time

Impulse = 200N x 8s = 1600Ns

To calculate final velocity of car,

Impulse = change in momentum

1600 = 700 (v-0)

1600 = 700v

v = 1600/700

v = 2.28 m/s

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the electric potential in a region of space varies as v=by/(a2+y2).PartA Determine the components of E Express your answers in terms of the variables a, b, and y separated by commas.

Answers

The electric potential in a region of space varies as v=by/(a2+y2) is derived to be (y2-a2)b/(a2+b2)^2.

What does "electric potential" presume?

Electric potential is the effort required to transport a unit charge from one point to another in the presence of an electric field.

Electric potential = E => dV/dx

                            E(x)  => d(by/a2+y2)/dx =>0

                           E(y)   => d(by/a2+y2)

                                   => (y2-a2)b/(a2+b2)^2

           

Does space have an electric field?

Maxwell's equations show that there is indeed an electric field in empty space. Maxwell was the first to demonstrate that the propagation speed of electromagnetic waves is comparable to that of light speed, leading to the conclusion that visible light and EM waves are identical.

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Samples of four group 15 elements, antimony, arsenic, bismuth, and phosphorus, are in the gaseous phase. An atom in the ground state of which element requires the least amount of energy to remove its most loosely held electron?.

Answers

An atom in the ground state that requires the least amount of energy to remove its most loosely held electron is Bi (Bismuth).

Why Bismuth requires least amount of energy to remove its most loosely held electron?

Bismuth atom has 83 electrons and the shell structure is as 2.8.18.32.18.5.  An atom in which total energy of the electrons can not be lowered by transferring one or more electrons to different orbitals is called as ground-state atom. We can say that, in this case all electrons are in the lowest possible energy levels.

Ground state electron configuration of ground state gaseous neutral Bismuth is as shown here : [Xe].4f^14.5d^10.6s^2.6p^3.

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calculate [d+] and [od−] for pure (neutral) d2o at this temperature.

Answers

The concentration of D+ and OD- ions for pure (neutral) D₂O is calculated to be [D+] = [OD-] = 2.98 × 10⁻⁸ M.

Given that,

Kw = 8.9 × 10⁻¹⁶

where, Kw is the equilibrium constant for the autoionization of water.

D₂O when undergoes ionization, it splits into D+ and OD- ions.

Kw can be written as,

Kw = [D+] [OD-] = x²

So, x = √(Kw) = √(8.9 × 10⁻¹⁶) = 2.9832 × 10⁻⁸ M

Thus, the required concentration of both the ions is equal and its value is equal to [D+] = [OD-] = 2.98 × 10⁻⁸ M.

The question is incomplete. The complete question is 'Deuterium oxide (D2O, where D is deuterium, the hydrogen-2 isotope) has an ion-product constant, Kw, of 8.9 x 10^-16 at 20 *C (degrees Celsius). Calculate [D+] and [OD-] for pure (neutral) D2O at this temperature.'

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If the valence electrons were removed, what would be the ion charge of the element? na = _____ -1 1 -3 3

Answers

Answer:

The charge would be +1

Explanation:

Because Na is in the first group of the periodic table, one valence electron will be removed. Therefore, it will have a charge of +1.

How fast, (vfx)q, will the quarterback be moving backward just after releasing the ball?

An 80-kg quarterback jumps straight up in the air right before throwing a 0.43-kg football horizontally at 15 m/s . How fast will he be moving backward just after releasing the ball?

Answers

Applying the momentum principle, v = 0.08 m/s.

The Momentum Principle controls how a system moves. This theory explains how a system modifies its motion in response to a net force. We note that there is no net force acting on objects moving in a straight path at constant speed.

p = m v . The equation demonstrates that momentum is directly related to an object's mass (m) and velocity (v). As a result, an object's momentum increases with increasing mass or velocity. The momentum of a large, swift object is larger than that of a small, slower object.

80 kg for the quarterback and 0.43 kg for the ball.

initially both together, but with a horizontal velocity of zero.

Final momentum is equal to 15*0.43 - 80v starting momentum (law of conservation of momentum)

6.45 = 80v

v = 0.08 m/s

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The torque produced by a motor overload that pulls the rotor out of synchronization is referred to as

Answers

The torque produced by a motor overload that pulls the rotor out of synchronization is referred to as synchronous torque.

Torque is nothing but the measure of force which causes an object to rotate about an axis.

A rotor is a moving component in the electric motor.

It is the type of torque acting on the shaft of a synchronous machine when the rotational speed of the rotor deviates from the synchronous speed by keeping the machine in synchronism.

The pull out torque is the maximum value of torque that allows a synchronous motor to remain in synchronism without pulling out of synchronism.

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If you leave school and walk 150 m Northeast to
the gas station to get a bag of Takis, then you
turn around and walk 275 m Southwest to the
corner of Gillet and W. Walnut, what is your
distance traveled? What is your displacement?

Answers

Answer:

Distance = 425 m

Displacement = 125 m

Explanation:

Distance =  total length traveled =  150 m + 275 m = 425 m

Displacement =  distance from point of origin (school) to end point (street corner) = 275 m - 150 m = 125 m

Note:  You walk to the gas station, turn around and walk in a straight line back to school then another 125 m to the street corner

A family's travel budget includes $984 for petrol and food. If a family dinner costs $60 and petrol costs $3. 40 per gallon, how many gallons of petrol can the family purchase if they purchase 13 meals?.

Answers

Suppose a family supper costs $60 and a gallon of gas costs $3.40. If the family buys 13 meals, they may purchase 60 gallons of gasoline.

By costs, what do you mean?

Costs are also the dollar amount of purchases made for use by a company or other reporting entity of supplies, resources, labor, products, equipment, and other items.

What are some costs?

The majority of operating expenses are expenses that depend more on time than they do on how much your company produces or sells. Rent and leasing charges, salary, energy prices, health, and repayments are a few examples of fixed costs.

Total budget = $984

Dinner cost = $90

Petrol cost = $3.40 per gallon

Number of meals = 13

Number of gallons of petrol = g

60(13) + 3.40g = 984

780 + 3.40 g = 984

3.40g = 984 - 780

3.40 g = 204

g = 204 / 3.40

g = 60.

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How high a hill can a car coast up (engine disengaged) if work done by friction is negligible and its initial speed is 128 km/h

Answers

In general, the higher the initial speed of the car and the lower the slope, the farther the car will be able to coast up, but it is impossible to give a definitive answer without variables such as the slope and mass of the car.

If the work done by friction is negligible and the car is coasting with the engine disengaged, then the only force acting on the car will be gravity. This means that the car will slow down as it goes up the hill due to the force of gravity acting against its motion. The height of the hill that the car can coast up will depend on the slope of the hill and the mass of the car, as well as the initial speed of the car and the coefficient of rolling resistance. However, it is difficult to give a precise answer without knowing the specific values of these variables.

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ou decide to travel across Asia your watch set to Hong Kong, China time 6pm, yet the sun appears to be two hour before its zenith. How many degrees have you traveled from China

Answers

Undergraduate programs can be found in a variety of fields, including business, technology, science, and engineering, as well as medicine and the humanities. They normally run four years.

Courses in medicine and dentistry can be completed in up to five years. In China, there are 13 statutory categories of academic degrees, including those in economics, law, education, fine arts, history, science, engineering, and medicine. These categories include bachelor's, master's, and doctoral degrees. When they enter college, more and more Chinese students are opting to study abroad. However, Chinese parents believe that the Chinese educational system is the greatest in the world at the elementary, middle, and high school levels.

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The original velocity V₁ = 27 m/s, and you
press the brakes and the car has an
acceleration a = -8.4 m/s2 (the sign -
indicates that the acceleration vector in
the opposite direction of the velocity
vector of the car). What missing known
terms should you also know you have to
use?

Answers

To solve this we must be knowing each and every concept related to velocity. Therefore, the missing terms we have to know is the initial velocity, distance and time taken.

What is velocity?

It is a vector assessment of an object's rate of motion and direction of motion. As a result, in order to calculate velocity using this definition, we must be familiar with both magnitude and direction.

The original velocity V₁ = 27 m/s, and press the brakes and the car has an acceleration a = -8.4 m/s2 (the sign - indicates that the acceleration vector in the opposite direction of the velocity vector of the car). The missing terms we have to know is the initial velocity, distance and time taken.

Therefore, the missing terms we have to know is the initial velocity, distance and time taken.

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if a car is traveling 81 km/h , how far (in meters) do they go after 48 min

Answers

Answer:

64.8 km

Explanation:

speed = distance/time

Distance = speed x time

(81 km)(1000 m/km) = 81,000 m

1 hr = 60 min

Distance = (81000 m/60 min)(48 min) = 64800 m = 64.8 km

According to Newton's second law of motion, when a net force acts on an object, the acceleration is A. zero. B. inversely proportional to the object's mass. C. independent of mass. D. inversely proportional to the net force. E. directly proportional to the object's mass.

Answers

I think it’s D but I’m not sure

PLEASSEE HELP NEED DONE TNIGHTT

Answers

A) 25.9 m/s
It’s A that’s is the answer
Your welcome
If wrong sorry

If you exert a force of 45 N to walk 3 m up a flight of stairs in 5 seconds, how much power do you use

Answers

Important Formulas:

[tex]w=Fd[/tex]

work(measured in joules) = force(measured in newtons) * distance(measured in meters)

[tex]p=\dfrac{w}{t}[/tex]

power(measured in watts) = work(measured in joules) / time(measured in seconds)

__________________________________________________________

Given:

[tex]F=45N[/tex]

[tex]d=3m[/tex]

[tex]t=5s[/tex]

[tex]p=?[/tex]

__________________________________________________________

Finding work:

[tex]w=Fd[/tex]

[tex]w=45\times3[/tex]

[tex]w=135J[/tex]

__________________________________________________________

Finding power:

[tex]p=\dfrac{w}{t}[/tex]

[tex]p=\dfrac{135}{5}[/tex]

__________________________________________________________

[tex]\fbox{p = 27 watts}[/tex]

A 745 kg race car experiences an applied force from the engine of 38900 N and a frictional force of 34000 N. How long does it take to go from rest to 21 m/s ?

Answers

The time taken for the car to reach the given speed is 3.2 seconds.

What is the time of motion of the car?

The time of motion of the car is determined from the acceleration of the car which is calculated by applying Newton's second law of motion.

Mathematically, the formula for Newton's second law of motion is given as;

F (net) = ma

where;

m is the mass of the cara is the acceleration of the car

The acceleration of the car is calculated from the net force acting on the car.

F (net) = F - Ff

where;

F is the applied forceFf is the force of friction

F (net) = 38,900 N - 34,000 N

F (net) = 4,900 N

Now, the acceleration of the car is calculated  by applying Newton's second law of motion as shown below;

a = F (net) / m

a = ( 4,900 N ) / ( 745 kg )

a = 6.58 m/s²

The time of motion of the car is calculated by applying the first kinematic equation as shown below.

v = u + at

where;

u is the initial velocity of the car = 0 (since the car moved from rest)

v = 0 + at

v = at

t = v / a

t = ( 21 m/s ) / ( 6.58 m/s² )

t = 3.2 s

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A child slides down an icy slop (ignore any friciton) from rest, the slop's height is 5.85 m. Find the speed of the child at the end of the slop

Answers

As the friction is ignored, the speed of the child at the end of the slop is 10.71 m/s

Using the law of the conservation of energy, the mechanical energy is conserved.

At the highest position, her kinetic energy is zero, while at the end of the slop, the potential energy is zero.

Potential energy = PE = mgh

Kinetic energy = KE = 1/2 mv²

Where:

m = mass

g = acceleration due to gravity = 9.8 m/s²

h = height = 5.85 m

v = velocity

PE = KE

mgh = 1/2 mv²

v² = 2gh

v² = 2 x 9.8 x 5.85 = 114.66

v = 10.71 m/s

Hence, the speed of the child at the end of the slop is 10.71 m/s

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You are standing near a set of train tracks and hear the whistle of a coming train. You look to your left and notice the train traveling from left to right at 150 miles per hour. Yea i know Bolt is standing at the end of the passenger car on the train and begins to run. To you standing still it appears that Usain Bolt is running at a speed of 177 miles per hour. How fast is Usain Bolt actually running relative to the train?

Answers

The relative speed of a two bodies moving in the same direction is the difference between the speed of two bodies. Here, the  speed of Bolt relative to the train is 27 miles /hr

What is relative speed?

The speed of an object can be related to the speed of another moving object which can be of same direction or opposite direction. The speed of a body calculated with respect to the speed  another body is called the relative speed.

Speed is the measure of distance covered per unit time. The units of speed can be m/s, kilometer/hour, miles/hour etc.

Given that speed of the train = 150 miles/h

speed of Usain Bolt = 177 miles/h

Both the train and bolt are moving in the left to right direction. Then the relative speed of bolt with respect to the train is:

177 - 150 = 27 miles/h

Therefore, Bolt runs with a speed of 27 mils/h relative to the train.

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What is concave mirror also called?

Answers

A concave mirror is also known as converging mirror because it converges the incident rays parallel to the principal axis to the focus of the mirror after reflection. Concave mirrors reflect light inward to one focal point

What is a Concave mirror ?

A concave mirror has an inward-curving reflective surface that faces away from the light source. Light is reflected inward by concave mirrors to a single focus point. Unlike convex mirrors, a concave mirror's created image exhibits a variety of picture types based on the object's distance from the mirror.

A concave mirror has an inward-curving reflective surface that faces away from the light source. Light is reflected inward by concave mirrors to a single focus point. Unlike convex mirrors, a concave mirror's created image exhibits a variety of picture types based on the object's distance from the mirror.

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Estimate the volume, v , of one sodium atom ( na ) using its metallic radius of 186 pm.

Answers

Utilizing its metal radius of 186 pm, one sodium atom's volume, or v, is equal to 26965110.857pm3.

What elements make up a sodium atom?

Sodium seems to be an element in the periodic table with the atomic number 11 and the symbol Na (derived from the Latin natrium). It is a delicate, silvery-white metal that is exceedingly reactive. Due to its placement in group one of the periodic table, sodium is very much an alkali metal. 23Na is the only stable isotope of it.

Is an atom of sodium a metal?

Alkali metal subgroup (Group 1 [Indeed is]) of the element element sodium (Na). The element sodium has a very delicate silvery-white.

volume of spherical sodium atoms,

V=4/3 πr³

Here,

volume = V

radius = r

The value of r is 186pm.

= (4/3) × (22/7) × (186pm)³

= (88/21)×6434856pm³

= 26965110.857pm³

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A box with mass m is sliding along on a friction-free surface at 9.87 m/s at a height of 1.81 m. It travels down the hill and then up another hill.
Find the speed at the bottom of the hill.
Find the maximum vertical height to which the box will rise on the opposite hill.
Please show your work.

Answers

(a) The speed at the bottom of the hill is 11.53 m/s.

(b) The maximum vertical height to which the box will rise on the opposite hill is 6.78 m.

What is the speed of the box at the bottom of the hill?

The speed of the box at the bottom of the hill is calculated by applying the following kinematic equation as shown below.

v² = u² + 2gh

where;

v is the final speed of the voxu is the initial speed of the bocg is acceleration due to gravityh is the height of the hill

v² = ( 9.87² ) + 2( 9.8 )( 1.81 )

v² = 132.89

v = √ ( 132.89 )

v = 11.53 m/s

The maximum vertical height to which the box will rise on the opposite hill is calculated by applying the principle of conservation of energy.

mgh = ¹/₂mv²

h = ( v² ) / ( 2g )

h = ( 11.53² ) / ( 2 x 9.8 )

h = 6.78 m

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A space heater is connected to a standard 120 volt line. If the resistance of the operating
heater is 12 ohms, what power does the heater use? (NOTE: you'll have to use both Ohm's
Law and the Power Equation.)

A) 1200 W

B) 0.10 W

C) 10 W

D) 1440 W

Answers

Answer:

A)  1200 W

Explanation:

First find I (current):

V = IR, so I = V/R

I = 120V/12Ω = 10 A

Now find P (power):

P = VI = (120V)(10A) = 1200 W

What happens to the energy in a Newton's cradle demonstration? Please respond in 1-2 complete
sentences using your best grammar.

Answers

Answer:
In Newton's Cradle Demonstration, converts the potential energy of one ball into kinetic energy, which is passed down the line of other balls and results of swinging the last ball upward.

Explanation:
The balls in the middle do not swing, they do move, however, because they absorb some of the kinetic energy from the left swinging ball.

The right side exterior ball moves out but not with 100% of the kinetic energy, it receives less than 100% due to interference. However, energy is transferred from the outside left swigging ball to the opposite right end ball which then swings away.

The balls that are touching in the middle cannot conduct 100% of the kinetic energy. Then additionally, gravity affects the right side swinging ball so that the kinetic it does receive through transference is affected by gravity resistance and air resistance. Thus, it swings out with less energy momentum than the left side swinging ball had coming down.

A ball of mass 9m is dropped from rest from a height H = 5.0 meters above the ground, as shown above on the left. It undergoes a perfectly elastic collision with the ground and rebounds. At the instant that the ball rebounds, a small blob of clay of mass m is released from rest from the original height H, directly above the ball, as shown above on the right. The clay blob, which is descending, eventually collides with the ball, which is ascending. Assume that g = 10 meters/second^2, that air resistance is negligible, and that the collision process takes negligible time. Determine the speed of the ball immediately before it hits the ground. Determine the time after the release of the clay blob at which the collision takes place. Determine the height above the ground at which the collision takes place. Determine the speeds of the ball and the clay blob immediately before the collision. If the ball and the clay blob stick together on impact, what is the magnitude and direction of their velocity immediately after the collision?

Answers

i. The speed of the ball immediately before it hits the ground is 10 m/s

ii. The time after the release of the clay blob is 1 s

iii. The height above the ground is 5.0 meters

iv. The speeds of the ball and the clay blob immediately before the collision are 10 m/s and 20 m/s respectively

v. The magnitude and direction of their velocity is (910 + m20)/(9+m) with upward directions.

How do we determine the values of the speeds, height and magnitude?

The speed of the ball immediately before it hits the ground can be determined using the equation:

v^2 = u^2 + 2as

where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration due to gravity (10 m/s^2), and s is the distance fallen (5.0 meters).

Substituting these values in gives:

v^2 = 0 + 2(10)(5) = 100

v = sqrt(100) = 10 m/s

The time after the release of the clay blob at which the collision takes place can be determined using the equation:

s = ut + (1/2)at^2

where s is the distance fallen (5.0 meters), u is the initial velocity (0 m/s), a is the acceleration due to gravity (10 m/s^2), and t is the time.

Substituting these values in gives:

5 = 0 + (1/2)(10)t^2

t = sqrt(5/5) = 1 s

The height above the ground at which the collision takes place is the same as the initial height, H = 5.0 meters.

The speeds of the ball and the clay blob immediately before the collision can be determined using the equations:

v = u + at

where v is the final velocity, u is the initial velocity (0 m/s), a is the acceleration due to gravity (10 m/s^2), and t is the time.

For the ball, t = 1 s and v = 10 m/s

For the clay blob, t = 2 s and v = 20 m/s

Since the collision is perfectly elastic, the total momentum before the collision is equal to the total momentum after the collision, and the kinetic energy before the collision is equal to the kinetic energy after the collision.

The magnitude and direction of their velocity immediately after the collision is the same as their center of mass velocity,

vcm = (m1v1+m2v2)/(m1+m2) = (910 + m20)/(9+m) and it is directed upwards.

Therefore, the correct answers are as given above.

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To find the change in the electric potential from point/to point f, which do we do? a. We find the ratio of the electric field to the distance between the points. b. We find the ratio of the distance between the points to the electric field. c. We integrate the negative of the electric field along a path from i to f. d. We integrate the negative of the electric field along a path from f to i. e. We differentiate the electric field with respect to distance along the path from i to f.

Answers

The correct option is the third option that is we integrate the negative of the electric field along a path from i to f.

We can find the electrostatic potential at any point due to each individual charge by considering the other charges absent. We then add all the charges algebraically. Hence, the electric potential at a point due to a group of point charges is the algebraic sum of all the potentials due to individual charges. To find the change in the electric potential from point/to point f, we have the following options a. We find the ratio of the electric field to the distance between the points. b. We find the ratio of the distance between the points to the electric field. c. We integrate the negative of the electric field along a path from i to f. d. We integrate the negative of the electric field along a path from f to i. e. We differentiate the electric field with respect to distance along the path from i to f. Hence with this information we can consider that the correct option is the third option that is we integrate the negative of the electric field along a path from i to f.

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