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A 2.9 g bullet moving at 309 m/s strikes a stationary block with a mass of 2.55 kg. If the bullet passes through the block and continues moving at a speed of 48 m/s, how fast is the block moving after the bullet hits it? Remember, the mass must be in kilograms. Report the answer to 4 decimal places. Please do not include units or the answer will be marked incorrect.
296.8235

Object A undergoes a head-on collision with Object B. If Object A was traveling at 1 m/s and has a mass of 4 kg, and Object B has a mass of 7 kg, how fast was Object B traveling if both objects come to rest after the collision? Report your answer to one decimal place. Please do not include units or the answer will be marked incorrect.
-0.6

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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(a) The velocity of the ball is 41.16 m/s.

(b) The height reached by the ball is 86.44 m.

Velocity is the rate of change of displacement.

(a) To calculate the velocity at which the pitcher throw the ball, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute thee values into equation 1

(b) To calculate how high the ball rise, we use the formula

Where:

Substitute into equation 2

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Answer: Limestone Caves

Explanation: The most common feature that can be caused purely by chemical weathering is Karst Landscape, which can lead to caverns and sinkholes.

Answer:

Approximately \(641\; {\rm N}\) (assuming that \(g = (-9.81)\; {\rm N \cdot kg^{-1}}\).)

Explanation:

Forces on this person:

Let \(m\) denote the mass of this person. It is given that \(m = 50\; {\rm kg}\). The weight of this person will be:

\(\begin{aligned}(\text{weight}) &= m\, g \\ &= (50\; {\rm kg})\, ((-9.81)\; {\rm N\cdot kg^{-1}}) \\ &\approx 490.5\; {\rm N}\end{aligned}\).

(The value of weight is negative since weight points downwards.)

Let \(a\) denote the acceleration of this person. It is given that \(a = 3\; {\rm m\cdot s^{-2}}\) (since this person is accelerating upwards, the value of \(a\) will be positive.) The net force on this person will be:

\(\begin{aligned}(\text{net force}) &= (\text{mass})\, (\text{acceleration})\\ &= (50\; {\rm kg})\, (3\; {\rm m\cdot s^{-2}}) \\ &\approx 150\; {\rm N}\end{aligned}\).

Note that this net force is also equal to the vector sum of all the forces on this person. In other words:

\(\begin{aligned}(\text{net force}) &= (\text{weight}) + (\text{normal force})\end{aligned}\).

Rearrange this equation to find \((\text{normal force})\):

\(\begin{aligned}(\text{normal force}) &= (\text{net force}) - (\text{weight}) \\ &\approx 150\; {\rm N} - ((-490.5)\; {\rm N}) \\ &\approx 641\; {\rm N}\end{aligned}\).

Hence, the upward force on this person from the floor of the elevator will be approximately \(641\; {\rm N}\).

Answer: current I = 1.875A

Explanation:

If the resistors are connected in series,

Then the equivalent resistance will be

R = 6 + 18 + 15 + 9

R = 48 ohms

Using ohms law

V = IR

Make current I the subject of formula

I = V/R

I = 90/48

I = 1.875A

And if the resistors are connected in parallel, the equivalent resistance will be

1/R = 1/6 + 1/18 + 1/15 + 1/9

1/R = 0.166 + 0.055 + 0.066 + 0.111

R = 1/0.3999

R = 2.5 ohms

Using ohms law

V = IR

I = 90/2.5

Current I = 35.99A

A skier has potential energy when they first start out. She only has kinetic energy just at bottom of the hill. At first, the skier is at rest, and all of his energy is potential energy.

Gravity transforms the ball's potential energy into motion as it roll down the ramp, such that when it reaches the bottom of a loop, its energy was zero and its velocity ((1/2)mv2) is at its highest.

When the child reaches the bottom of a slide, they have both thermal and kinetic energy since a portion of the energy is heated by friction. We can make the energy merely at the beginning to finish equal in accordance with the energy conservation legislation.

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The velocity of this automobile as a function of time. At t = 5 seconds, the automobile is 90 meters from its initial position.

To determine the distance traveled by the automobile from its t = 0 initial position, we need to calculate the area under the velocity-time graph up to t = 5 seconds.

The graph shows the velocity of the automobile as a function of time. Let's assume that positive velocity represents forward motion, and negative velocity represents backward motion.

Since velocity represents the rate of change of displacement, the area under the velocity-time graph represents the displacement or distance traveled. In this case, the area will consist of two parts: the area above the x-axis (forward motion) and the area below the x-axis (backward motion).

To calculate the area, we can break it down into two separate integrals:

1. The area above the x-axis (forward motion):

Since the velocity is constant at 20 m/s for the first 4 seconds, the area is a rectangle:

Area1 = velocity * time = 20 m/s * 4 s = 80 m

2. The area below the x-axis (backward motion):

The velocity changes to -10 m/s at t = 4 seconds. From t = 4 seconds to t = 5 seconds, the velocity is -10 m/s. The area is a rectangle:

Area2 = velocity * time = -10 m/s * 1 s = -10 m

To find the total distance traveled, we add the absolute values of the areas:

Total distance = |Area1| + |Area2| = |80 m| + |-10 m| = 80 m + 10 m = 90 m

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The net force on the top charge due to the other two charges is zero, and the charge will remain in equilibrium.

We can use Coulomb's law to calculate the force exerted by one charge on another. Coulomb's law states that the magnitude of the electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Mathematically, it can be expressed as:

F = (kq1q2)/r^2

where;

In this case, we have three charges of equal magnitude q placed at the vertices of an equilateral triangle of side length 1. We can calculate the distance between any two charges using the geometry of the equilateral triangle. The distance between any two adjacent charges is 1, and the distance between any two opposite charges is √3.

Let's consider the force exerted on one of the charges, say the one at the top of the triangle, due to the other two charges at the bottom left and bottom right vertices. The distance between the top and bottom left charges is 1, and the distance between the top and bottom right charges is also 1.

Therefore, the magnitude of the force exerted by the bottom left charge on the top charge is:

F1 = (kqq)/1^2 = k*q^2

Similarly, the magnitude of the force exerted by the bottom right charge on the top charge is also k*q^2. Since the two forces are acting in opposite directions along the same line, we can simply subtract them to find the net force:

F_net = F1 - F2 = kq^2 - kq^2

F_net = 0

Therefore, the net force on the top charge due to the other two charges is zero, and the charge will remain in equilibrium.

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GalileoGalilei is known as the father of science

The polynomial relationship between position and time for the bowling ball is linear.

A linear relationship between two variables is a term used to describe a straight-line relationship between the two variables.

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

From the equation of linear relationship between two variable, the highest power of x is one.

The given equation for position and time;

x(t) = vot + xo

From this given equation, the highest power of t is one, hence it is called linear relationship.

Thus, the polynomial relationship between position and time for the bowling ball is linear.

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Answer:

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Explanation:

The change of temperature at absolute scale is. A. 3.73 K

Answer:

373K

Explanation:

300°c - 200°c =100°c

Absolute scale means Kelvin scale so

0°c= 273°c

100°c = 100 + 273

=373K

According to the Keynesian view, manipulating foreign sector spending is not a reliable way to move the U.S. economy toward a more acceptable equilibrium because it does not address the fundamental causes of economic instability.

Keynesian economics focuses on the role of domestic demand in driving economic growth and stability. The government can use fiscal and monetary policy to stimulate aggregate demand and promote full employment. However, changes in foreign sector spending can be unpredictable and beyond the control of domestic policymakers. For instance, an increase in foreign demand for U.S. exports could boost economic growth and employment in the short run, but it may not be sustainable if the foreign demand later decreases. Similarly, a decrease in foreign demand for U.S. exports could have negative short-term effects on the economy, but it may not necessarily lead to a long-term decline. In short, Keynesian economics emphasizes the importance of domestic demand management and stabilizing the economy through government intervention. While changes in foreign sector spending can have some impact on the economy, they are generally seen as unreliable and unpredictable, and therefore not a reliable tool for achieving economic stability in the long run.

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The second step of the scientific method is to form a hypothesis. Thus, the correct option for this question is A.

A scientific method may be defined as the complete procedure through which the objectives of any experiment are established facts through testing and experimentation. There are numerous steps of the scientific method exist.

The basic steps of the scientific methods are as follows:

It is a systematic and well-regulated approach that involves in obtaining information about a scientific nature or obtaining a desired material or product.

Therefore, the second step of the scientific method is to form a hypothesis. Thus, the correct option for this question is A.

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Answer:

The axis of rotation of the Earth is tilted at an angle of 23.5 degrees away from vertical, perpendicular to the plane of our planet's orbit around the sun. The tilt of the Earth's axis is important, in that it governs the warming strength of the sun's energy.

Explanation:

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Since he runs a company in the US He exchanges goods and services with parties, Jack is engaged in international trade.

International trade is the exchange of goods and services between countries. It is a major driver of economic growth and prosperity. Jack's company can benefit from international trade in a number of ways. First, it can access new markets and customers. Second, it can source lower-cost inputs from other countries. Third, it can diversify its risk by selling to customers in multiple countries.

However, Jack's company also faces some challenges when engaging in international trade. First, it must deal with different languages, cultures, and legal systems. Second, it must comply with import and export regulations. Third, it must manage the risk of currency fluctuations.

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Answer:

The answer is Non contract force

Answer:

The  value \(y = 0.0349 \ m\)

Explanation:

From the question we are told that

   The  distance of the screen is  \(D = 2.30 \ m\)

   The  width of the slit is  \(d = 0.0368 \ nm = 0.0368 *10^{-3} \ m\)

   The  wavelength is  \(\lambda = 558 \ nm = 558 *10^{-9} \ m\)

The  width of the central diffraction peak is  mathematically represented as

        \(k = 2 * y\)

Where  y is the distance from the center to the high peak which  is mathematically represented as

       \(y = \frac{\lambda * D }{d }\)

substituting values

      \(y = \frac{ 558 *10^{-8} * 2.30 }{0.0368 *10^{-3} }\)

      \(y = 0.0349 \ m\)

Answer:

and?????

Explanation:

Answer:

1 m/s^2

Explanation:

F=ma

2 Newtons=2 Kg * a

a=1 m/s^2

A box puts a pressure of 50 N/\(m^{2}\) on an area of 0.25 \(m^{2}\). The force of the box on the floor is 12.5 Newton (N)

Pressure is defined as the physical force exerted on an object. The force applied is perpendicular to the surface of objects per unit area. The basic formula for pressure is \(\frac{F}{A}\) (Force per unit area). Unit of pressure is Pascals (Pa). Types of Pressures are Absolute, Atmospheric, Differential, and Gauge Pressure.

Using the formula Force = Pressure × Area

given Pressure = 50 N/\(m^{2}\)

area = 0.25 \(m^{2}\)

Substituting the values ,

Force = 12.5 Newton

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Answer:

B:A

Explanation:

because the alphabet goes

A B C D E F G

Answer: B.) A

This was a little complicated because of the answer letters LOL

The minimum coefficient of static friction with the floor is 0.3846.

To find the minimum coefficient of static friction with the floor, we need to consider the forces acting on the couch. In this case, the force of gravity is pulling the couch downward with a magnitude of mg, where m is the mass of the couch (40 kg) and g is the acceleration due to gravity (9.8 m/s²).

Since the couch does not move, the force of static friction between the couch and the floor must be equal in magnitude but opposite in direction to the horizontal pushing force of 150 N.

Therefore, we have the equation F_friction = F_push, where F_friction is the force of static friction.

The force of static friction can be calculated using the formula F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.

Since the couch is on a level floor and is not accelerating vertically, the normal force N is equal in magnitude but opposite in direction to the force of gravity, which is mg.

Substituting the values into the equation, we have μs * mg = 150 N.
Solving for μs, we get μs = 150 N / (mg).
Substituting the given values, we have μ_s = 150 N / (40 kg * 9.8 m/s²).
Simplifying, we find that μs = 0.3846.

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Answer:

3.962

Explanation:

mass = 1.2

gravity g = 9.81

velocity = ?

mgh = 1/2mv² + 1/2(1/2)mv²

= 9.81 x 1.2  = 3/4v²

11.772 x 4 = 3/4v²

47.088 = 3v²

divide through both sides by 3

15.696 = v²

take the square root of both sides

√15.696 = √v²

= 3.6962 = v

the speed is therefore 3.692

The mass of the heavy block moved at a constant speed is determined as 30.61 kg.

The mass of the rock is determined from the weight of the block. The weight of the block is the product of mass and acceleration due to gravity.

W  = mg

m = W/g

where;

m = (300)/(9.8)

m = 30.61 kg

Thus, the mass of the heavy block moved at a constant speed is determined as 30.61 kg.

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Answer:

The one with the faster velocity is the one with a velocity of -10m/s

When reading the simile "Bolt runs as fast as lightning," the most appropriate visual interpretation would be that "Bolt runs very fast."

This simile compares Bolt's speed to that of lightning, which is known for its incredible swiftness. The intention is to emphasize Bolt's exceptional speed by equating it to the rapid movement of lightning.

While the simile highlights Bolt's remarkable speed, it does not specify the manner in which he runs or the impact of each step. Therefore, the options suggesting Bolt runs in a straight line, in a wavy manner, or that each step produces thunder are not directly implied by the simile itself. These additional details go beyond the comparison of speed and introduce elements that are not explicitly mentioned.

Hence, the most accurate interpretation based solely on the simile is that Bolt runs very fast, comparable to the speed of lightning.

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A VfL (Vertical Field LED) backlighting system is commonly used in LCD (Liquid Crystal Display) televisions.

LCD TVs rely on a backlight to illuminate the liquid crystal layer, which controls the passage of light to create the visual image. The VfL technology is a specific type of LED backlighting arrangement used in certain LCD TV models. In a VfL backlighting system, the LEDs (Light-Emitting Diodes) are positioned vertically along the edges of the LCD panel.

The light emitted by these LEDs is directed across the panel using light guides or optical films, illuminating the liquid crystal layer uniformly. One advantage of VfL backlighting is its ability to provide consistent illumination across the LCD panel, reducing any potential inconsistencies in brightness or color uniformity. The vertical orientation of the LEDs allows for more precise control over light distribution, improving overall image quality.

Additionally, VfL backlighting offers potential advantages in terms of power efficiency. By selectively dimming or turning off specific zones of LEDs, local dimming techniques can be employed to enhance contrast and black levels, resulting in improved picture quality while conserving energy. It's important to note that VfL backlighting is just one of several backlighting technologies available for LCD TVs.

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Answer:

A. The horizontal component of the hammer's velocity just as it leaves the roof can be calculated by multiplying the velocity of the hammer by the cosine of the angle of the roof with the horizontal:

Vhorizontal = V * cos(45) = 4.5 m/s * cos(45) = 3.16 m/s

B. The vertical component of the hammer's velocity just as it leaves the roof can be calculated by multiplying the velocity of the hammer by the sine of the angle of the roof with the horizontal:

Vvertical = V * sin(45) = 4.5 m/s * sin(45) = 3.16 m/s

Explanation:

Jonathan needs to maintain a separation of 0.543 mm between the plates to get the desired charge, and a dielectric constant of 92.6 to achieve a separation of 5 mm with a dielectric.

(a) Using the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage, we can solve for the capacitance: C = Q/V =\((8.15 x 10^-9 C) / (50 V) = 1.63 x 10^-10 F.\)

Then, using the formula for capacitance of parallel plate capacitors: C = ε0A/d, where ε0 is the permittivity of free space, A is the area of the plates, and d is the separation distance, we can solve for the separation distance: d =\(_{3}OA/C = (8.85 x 10^-12 F/m) x (0.01 m^2) / (1.63 x 10^-10 F) = 0.543 mm.\)

(b) To find the dielectric constant, we can use the formula for capacitance of a parallel plate capacitor with a dielectric: C = εrε0A/d, where εr is the relative permittivity or dielectric constant of the material. Solving for εr, we get: εr = Cd / ε0A = \((1.63 x 10^-10 F)\) x (0.005 m) / \((8.85 x 10^-12 F/m)\) x \((0.01 m^2)\) = 92.6.

Therefore, Jonathan should use a dielectric with a relative permittivity of 92.6 to achieve a separation of 5 mm.

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