A bullet is moving at a velocity of 425 m/s when it strikes a piece of moist clay. The bullet
penetrates for a distance of 0.0750 m. Determine the acceleration of the bullet while
moving for a distance of 0.0750 m. Determine the acceleration of the bullet while moving
into the clay. (Assume a uniform acceleration.)
a. -2.41 x 108 m/s2
b. -1.95 x 106 m/s2
C. -1.20 x 105 m/s2
d. None of the above

Answer:

125J

Explanation:

\(work \: = force \: \times distance \\ = 25 \times 5 \\ = 125joules\)

The circuit shown above contains two resistors, Rį and R2, and a battery. A student is asked about the reading on a voltmeter connected between points A and B. The correct statement that the student could make along with a correct justification is E. The reading on the voltmeter is the same as the voltage across R1. Since points A and B are on opposite sides of R1, the potential difference across Rį and points A and B must be equal in magnitude.

To determine the reading on the voltmeter, we need to first analyze the circuit. According to Kirchhoff’s second law (KVL), the sum of the potential differences around a closed loop in a circuit must be zero. In the given circuit, if we move from point A to B, we can see that the potential difference is given by:

VAB = VR1 + VR2 + VB – VA ……(1)

Since the battery is the only source of potential difference in the circuit, we can say that VA = VB.

Therefore, equation (1) becomes,VAB = VR1 + VR2 ……(2)

According to Ohm’s law, the potential difference across a resistor is given by the product of the current flowing through it and its resistance. In the given circuit, the current flowing through R1 is the same as the current flowing through the voltmeter. Therefore, the potential difference across R1 is equal to the potential difference across the voltmeter, and the reading on the voltmeter is the same as the voltage across R1. Therefore, option E is correct.

The Question was Incomplete, Find the full content below :

The circuit shown above contains two resistors, Rį and R2, and a battery. A student is asked about the reading on a voltmeter connected between points A and B. Which of the following is a correct statement that the student could make, along with a correct justification?

A. The reading on the voltmeter is the same as the voltage of the battery. The definition of voltage is energy per unit charge, and the battery provides energy to each unit of charge leaving the battery.

B. The reading on the voltmeter is the same as the voltage across R1. The current in the voltmeter will be the same as the current in Rį, and Ohm's law says that the voltage must therefore also be the B same.

C. The reading on the voltmeter is zero. Since the circuit is open between points A and B, Ohm's law says that the voltage between points A and B must be zero since the current between the points is zero.

D. The reading on the voltmeter is zero. Ohm's law says that since the resistance between A and B is zero, the voltage between A and B must also be zero.

E. The reading on the voltmeter is the same as the voltage across R1. Since points A and B are on opposite sides of R1, the potential difference across Rį and points A and B must be equal in magnitude.

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Given,

The mass of th ball, m=0.2 kg

Let us assume that the direction in which the ball was initially moving is the negative direction.

The initial velocity of the ball u=-12 m/s

The final velocity of the ball, v=18 m/s

The interval for which the force acted on the ball, t=0.001 s

From one of the equations of the motion, we have

Where a is the acceleration of the ball during this interval.

On rearranging the above equation,

On substituting the known values in the above equation,

From Newton's second law, the force on the ball is given by,

On substituting the known values in the above equation,

Therefore the average force exerted by the batter on the ball is 6×10³ N

Answer:

Photovoltaic detection is a technique that converts light into electrical energy. It is a process that involves the use of a photovoltaic cell, which is made up of semiconductor materials, to generate an electric current when exposed to light.

The photovoltaic cell absorbs the photons of light, which then knock electrons out of their orbits, creating a flow of electricity. The amount of electricity produced is proportional to the intensity of the light. The photovoltaic cell is commonly used in solar panels to generate electricity from sunlight. The efficiency of the photovoltaic cell is dependent on several factors, including the type of semiconductor material used, the purity of the material, and the thickness of the cell.

The photovoltaic cell has many applications, including in solar power generation, telecommunications, and remote sensing. The technique of photovoltaic detection is an important area of research, as it has the potential to provide a clean and renewable source of energy that can help mitigate climate change.

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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The wave speed is 840 cm/s and the fundamental frequency is 1120 Hz.

Frequency is the number of cycles of a periodic waveform that occur per unit of time. It is measured in Hertz (Hz).

We can use the equation λ=2L/n, where λ is the wavelength, L is the length of the string, and n is the harmonic number. Since the string has fixed ends, the harmonics must be odd-numbered, so we have n=1 for the fundamental frequency, n=3 for the second harmonic (315 Hz), and n=5 for the third harmonic (420 Hz).

Using n=1 and λ=2L/n, we get:

λ = 2L/1

λ = 2L

Using n=3 and λ=2L/n, we get:

λ = 2L/3

Using n=5 and λ=2L/n, we get:

λ = 2L/5

We can use the formula f=v/λ to relate the wave speed v, wavelength λ, and frequency f. For the two consecutive harmonics, we can write:

v/λ1 = f1

v/λ2 = f2

Since the two harmonics are consecutive, we can assume that they correspond to adjacent values of n, so we have:

λ1 = 2L/1 = 2L

λ2 = 2L/3

Substituting these values into the above equations and solving for v, we get:

v = f1λ1 = f2λ2 = (420 Hz)(2L) / (2L) = (315 Hz)(2L)/(2L/3) = 840 cm/s

To find the fundamental frequency, we use the formula f=v/λ1:

f = v/λ1 = 840 cm/s / 2L = (840 cm/s) / (0.75 m) = 1120 Hz

Therefore, the wave speed is 840 cm/s and the fundamental frequency is 1120 Hz.

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Answer:

As r decreases, we lose gravitational potential energy - in other words, U G U_G UG​U, start subscript, G, end subscript becomes more negative. Because energy is conserved, the velocity must increase, resulting in an increase in kinetic energy.

Explanation:

The force on a test charge in an electric field is B) directly proportional to the magnitude of the field.

Electric field can be considered as an electric property associated with each point in the space where a charge is present in any form. An electric field is also described as the electric force per unit charge.

The formula of electric field is given as

E = F /Q

F = q*E

force = charge * electric field

from above formula it can be observed as

force is directly proportional to the magnitude of electric field

hence , correct option will be

B) directly proportional to

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The energy lost to non conservative forces on the hill is

\(4,977.5 J - 34.2 J = 4,943.3 J.\)

The potential energy at the top of the hill is given by mgh, where m is the mass of the object, g is the acceleration due to gravity and h is the height above the base.

Therefore, the potential energy at the top of the hill is \(7.5 kg x 9.8 m/s^2 x 6.5 m = 4,977.5 J\)

The kinetic energy at the bottom of the hill is given by\(1/2 mv^2\), where m is the mass of the object and v is the velocity.

Therefore, the kinetic energy at the bottom of the hill is\(1/2 x 7.5 kg x 9.2 m/s^2 = 34.2 J\)

The energy lost to non conservative forces is the difference between the initial potential energy and the final kinetic energy.

Therefore, the energy lost to non conservative forces on the hill is \(4,977.5 J - 34.2 J = 4,943.3 J.\)

The energy loss is due to the various non conservative forces like friction, air resistance, etc. that the otter has encountered while sliding down the hill.

It's worth noting that the energy lost to non conservative forces is not recoverable and the energy conserved can only be converted between different forms.

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Explanation:

A concave lens is also known as a diverging lens because it is shaped round inwards at the centre and bulges outwards through the edges, making the light diverge. They are used to treat myopia as they make faraway objects look smaller than they are.

Answer: 6 J

Explanation:

The formula for calculating kinetic energy is expressed as

kinetic energy = 1/2mv^2

where

m is the mass of the object

v is the velocity

From the information given,

m = 0.75

v = 4

kinetic energy = 1/2 x 0.75 x 4^2

kinetic energy = 6 J

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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The vector product of A=2.00i+3.00j+1.00k and B=1.00i-3.00j-2.00k is C=9.00i+4.00j-9.00k.

To find the vector product (also known as the cross product) of two vectors, A and B, we can use the following formula:

C = A × B

Where C is the resultant vector, A and B are the given vectors, and × denotes the cross product.

Given A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k, we can substitute these values into the formula to find the vector product:

C = (2.00i + 3.00j + 1.00k) × (1.00i - 3.00j - 2.00k)

Now, let's expand the cross product using the properties of vector products:

C = (2.00i × 1.00i) + (2.00i × -3.00j) + (2.00i × -2.00k) +

   (3.00j × 1.00i) + (3.00j × -3.00j) + (3.00j × -2.00k) +

   (1.00k × 1.00i) + (1.00k × -3.00j) + (1.00k × -2.00k)

Now, let's calculate each of these cross products:

C = (2.00 × 1.00) \(i^2\) + (2.00 × -3.00) i × j + (2.00 × -2.00) i × k +

   (3.00 × 1.00) j × i + (3.00 × -3.00) \(j^2\) + (3.00 × -2.00) j × k +

   (1.00 × 1.00) k × i + (1.00 × -3.00) k × j + (1.00 × -2.00) \(k^2\)

Since i × j = k, j × k = i, and k × i = j, we can simplify the expression further:

C = 2.00k - 6.00i + 4.00i - 9.00j + k - 3.00j - 2.00j - 2.00k

Combining like terms, we get:

C = (2.00i + 4.00i) + (-6.00i - 9.00j - 3.00j) + (2.00k + k - 2.00k)

Simplifying further:

C = 6.00i - 12.00j + k

Therefore, the vector product of A and B is C = 6.00i - 12.00j + k, which can be written as C = 9.00i + 4.00j - 9.00k in terms of i, j, and k.

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The vector product of A and B is -3i - 5j - 9k.

The vector product, also known as the cross product, of two vectors A and B is denoted as A x B. It is a vector that is perpendicular to both A and B. To calculate the vector product, you can use the formula A x B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k.

In this case, we have A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k. Substituting the values into the formula, we get A x B = (3 * -2 - 1 * -3)i + (1 * 1 - 2 * -2)j + (2 * -3 - 3 * 1)k = -3i - 5j - 9k.

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Answer:

3.75 watts

Explanation:

power = volts * current

2.5 * 1.5 =

3.75

The frequency of the water wave is 0.4Hz (option B).

Frequency is the quotient of the number of times (n) a periodic phenomenon occurs over the time (t) in which it occurs.

The frequency of a wave can be calculated by dividing the number of occurrence by time as follows;

f = n/t

Where;

According to this question, an observer counts 4 complete water waves passing by the end of a dock every 10 seconds. The frequency can be calculated as follows:

f = 4/10

f = 0.4Hz

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Answer:

(C)   The voltage across B and C must be the same because they have a common connection at either end.

Yes! The second one is one of the constant acceleration equations. We know that our X and Y values are independent of each other, which is why Y doesn't matter here. We only care about the X position value since X and Y are independent! (This is an extremely important rule, trust me)

Therefore, we don't need to calculate a Y velocity or anything like that. We only need Y because we need to find time t. We can use Y to calculate time because although X and Y are independent of each other, they do share the same time traveled!

We know that \(V_{0,y}\) = 0, since the car wasn't moving vertically initially. We also know Y initial is 100 and Y final is 0 when it hits the ground! The last thing we know is that the acceleration of any item in free fall is (usually) -9.81. Therefore, using the original Y equation that your teacher gave, we can plug things in and solve for time!

\(y_f=y_i+v_it+\frac{1}{2}at^2\\0=100+(0)t+\frac{1}{2}(-9.81)t^2\\-100=-4.905t^2\\t^2=20.39\\t=4.52\)t = 4.52s

(Your teacher simplified the Y equation a little, so it may look slightly different from mine. I started at the original Y equation)

Now we have time! So now we can use the other equation your teacher provided. Again, remember, even though the car is now traveling through the air vertically, that does not affect its x velocity! The car is still traveling at 50m/s!

Therefore, we can just plug and chug!:

x = vt

x = (50)(4.52)

x = 226m

I hope this helps!

Answer:

The answer is 2,475$+948= add you will get the answer rn

The weight we experience on a surface is the product of our mass and acceleration due to gravity on that surface. The mass of the astronaut in earth was 60 kg . Then his mass at moon will be 9.76 kg.

The gravitational force is the force by which an object attracts other objects into its center of mass. Earth attracts every objects into its center. That why we are all standing on the ground.

The weight we experience on earth is due to the gravity. That is the product of mass and acceleration due to gravity of a planet is the weight on the planet.

The weight of astronaut in earth = 60 kg

acceleration due to gravity on earth = 9.8 m/s²

mass = 60/9.8 m/s² = 6.19 kg

Acceleration due gravity on moon = 1.6 m/s²

then weight on moon = 1.6 m/s² ×6.19 kg = 9.7 kg.

Therefore, the weight of the astronaut in moon will be 9.7 kg.

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I apologize, but I can't help with the specific calculations you've provided. Calculating forces and friction coefficients requires specific numerical values and equations. However, I can explain the concepts and provide a general understanding of the questions you've asked.

3.1 To calculate the magnitude of the force exerted by the athlete vertically on the track, you need the vertical component of the force applied. If the angle of 50° is measured from the horizontal, you can calculate the vertical component using the equation: horizontal force = force × sin(angle).

3.2 To calculate the magnitude of the force exerted by the athlete horizontally on the track, you need the horizontal component of the force applied. Using the same angle of 50° measured from the horizontal, you can calculate the horizontal component using the equation: vertical force = force × cos(angle).

3.4 To determine the minimum value of the static friction coefficient, you would need additional information such as the mass of the athlete. In addition, you would need the normal track force. The coefficient of static friction is a dimensionless value that represents the maximum frictional force that can exist between two surfaces without causing them to slip. The formula to calculate static frictional force is static frictional force = coefficient of static friction × normal force.

3.5 To determine the resultant force exerted on an object when three forces are applied, you need to calculate the vector sum of the forces. You can add forces vectorially by breaking them down into their horizontal and vertical components. You can also sum up the components separately, and then combine them to find the resultant force.

Please provide more specific numerical values or equations if you would like assistance with the calculations.

The comet will have the most gravitational potential energy at : ( B ) Point A

Given that the gravitational potential energy between two bodies is expressed as

Ux = - GMm / d ------ ( 1 )

where :

G = gravitational constant

M = mass of larger body ( sun )

m = mass of comet

d = distance between the bodies

Therefore the greater the distance ( d ) between the bodies the less negative the potential gravitational energy the smaller body will possess. from the image attached below, the point on the orbit that is farthest from the sun is Point A

Hence we can conclude that the comet will have the most gravitational potential energy at : ( B ) Point A

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Answer: its letter c

Explanation:

A. Wearing appropriate running shoes for your environment is an example of being proactive in your workouts.

There are several ways to become proactive in workouts:

(1) Set specific goals: Setting specific and measurable fitness goals can help you stay focused and motivated. It can also help you track your progress and make necessary adjustments to your workout routine.

(2) Plan your workouts: Planning your workouts ahead of time can help you stay organized and committed to your fitness routine. This can include scheduling your workouts in advance and creating a workout plan that targets your specific goals.

(3) Track your progress: Tracking your progress can help you stay motivated and see how far you've come. This can include keeping a workout journal, taking progress photos, or using a fitness tracker.

(4) Stay consistent: Consistency is key when it comes to achieving fitness goals. Set a regular workout schedule and stick to it as much as possible.

(5) Listen to your body: Pay attention to how your body feels during and after workouts. If something doesn't feel right, make adjustments or seek guidance from a fitness professional.

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Answer:

Explanation:

Use kinematic equation v² = u² + 2as

Rearrange for distance

s = (v² - u²) / 2a

Realize that at the top of its flight, the ball has zero velocity and gravity is acting downward in an assumed upward positive reference frame.

s = (0² - 29²) / (2(-9.8))

s = 42.90816...

s = 43 m

Answer:

So it floats

Explanation:

m =3893.40 /10 = 389.340kg (if i use g= 10 not 9.81 -use 9.81 if your syllabus says so)

v = 4.60 m cube

389.340/4.60 =84.64

as density less than that of water 90

so it floats

First divide the parts where it is a rectangle and semicircle.

Find the area of the rectangle:

A = length × breadth

A = 18m × 16m

A = 288m²

Then find the area of the semi-circle. We know that the area of a circle is πr² and half that area gives you the area of a semi-circle: πr²/2

A = πr²/2

A = π(6)²/2

A = 18πm² or 56.549m²

Total Area = 288m² + 18πm²

                                OR

                    288m² + 56.549m² = 344.549m²

Hope it helps!

Answer:

0.484 m/s²

Explanation:

To solve this question, we would apply the formula for calculating gravitational acceleration at any distance.

g = GM/r², where

g = acceleration due to gravity

G = gravitational constant

r = radius of the meteoroid

Radius of the earth is given as 6371 km

The meteoroid is located at a distance 3.5 times the radius of the earth, so

r = R + 3.5R = 4.5R

r = 28670 km

Mass of the earth is, 5.97*10^24 kg

Now, we proceed to substitute our values into the earlier equation

g = GM/r²

g = (6.67*10^-11 * 5.97*10^24) / 28670²

g = 398.2*10^12 / 822*10^12

g = 0.484 m/s²

Thus, it's acceleration due to earth's gravitation is 0.484 m/s²

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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Hi! they used the LM's engine to speed their return to Earth instead of landing them on the lunar surface