A ball thrown with 50N of force accelerates at 25 m/s2.  What is the mass of the ball?

Rounded to two significant figures, the initial activity of the sample was approximately 390000 μCi.

We have,

The decay of a radioactive substance follows an exponential decay formula:

N(t) = N₀ [tex](1/2)^{t / T},[/tex]

where:

N(t) is the quantity of the substance remaining at time t.

N₀ is the initial quantity of the substance.

t is the time that has passed.

T is the half-life of the substance.

In this case, we are given:

Half-life (T) = 32.5 days,

Activity after 97.5 days (N(97.5d)) = 3.1 Ci.

Since activity (A) is proportional to the quantity of the substance

(A = λ * N), we can write:

[tex]A(t) = A_0 ~(1/2)^{t / T},[/tex]

where:

A(t) is the activity at time t.

A₀ is the initial activity.

Given that A(97.5d) = 3.1 Ci, we can substitute the values and solve for A₀:

3.1 Ci = A₀ x [tex](1/2)^{97.5d / 32.5d}.[/tex]

Solving for A₀:

[tex]A_0 = 3.1 Ci / (1/2)^{97.5d / 32.5d}\\A_0= 3.1 Ci / (2^{3)}.[/tex]

Calculating:

A₀ ≈ 0.3875 Ci.

Now, we need to convert this to microcuries (μCi):

1 Ci = [tex]10^6[/tex] μCi,

So,

A₀ = 0.3875 Ci x [tex]10^6[/tex] μCi/Ci ≈ 387500 μCi.

Thus,

Rounded to two significant figures, the initial activity of the sample was approximately 390000 μCi.

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The complete question:

The radioactive decay of cesium-141 (Ce-141) has a half-life of 32.5 days. After 97.5 days have elapsed, a sample of Ce-141 has an activity of 3.1 curies (Ci). What was the initial activity, in microcuries (μCi), of the sample? Provide your answer using two significant figures.

To find the initial activity of the sample, we can use the concept of radioactive decay and the given half-life and activity measurements.Rounding to two significant figures, the initial activity of the sample is approximately 2.5 * 10^7 microcuries (μCi).

1. The half-life of cesium-141 (Ce-141) is 32.5 days, which means that every 32.5 days, the activity of the sample is reduced by half.

2. After 97.5 days, the activity of the sample is measured to be 3.1 curies (Ci).

To find the initial activity, we need to determine how many half-lives have occurred in 97.5 days. We can do this by dividing 97.5 days by the half-life of 32.5 days.

3. 97.5 days ÷ 32.5 days = 3 half-lives.

Since each half-life reduces the activity by half, three half-lives will reduce the activity to (1/2) * (1/2) * (1/2) = 1/8 of the initial activity.

4. Therefore, the current activity is 1/8 of the initial activity.

Given that the current activity is 3.1 curies (Ci), we can find the initial activity by multiplying the current activity by 8.

5. 3.1 curies * 8 = 24.8 curies.

To convert the activity to microcuries (μCi), we can multiply by 10^6 since 1 curie is equal to 10^6 microcuries.

6. 24.8 curies * 10^6 = 2.48 * 10^7 microcuries (μCi).

Rounding to two significant figures, the initial activity of the sample is approximately 2.5 * 10^7 microcuries (μCi).

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The best place to store a fire extinguisher on a boat is in an easily accessible and visible location. It should be secured to prevent it from moving during rough seas.

The best place to store a fire extinguisher on a boat is in an easily accessible and visible location. It should be placed in an area where it is not likely to be damaged or obstructed. Common locations include near the helm, in the galley, or in the engine compartment. It is important to secure the fire extinguisher with mounting brackets or straps to prevent it from moving during rough seas.

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The maximum altitude reached by the rocket is 334.2 meters, and the total time elapsed from takeoff until the rocket strikes the ground is 16.55 seconds.

To find the maximum altitude reached by the rocket, we need to consider two stages: the powered ascent and the free-fall descent. During the powered ascent, the rocket accelerates upwards at a constant acceleration of 52.7 m/s2 for 1.41 seconds.

Using the kinematic equation for displacement: s = ut + (1/2)at2, where 's' is displacement, 'u' is initial velocity (0 m/s in this case, as it starts from rest), 'a' is acceleration, and 't' is time, we get:

s = 0 m/s * 1.41 s + 0.5 * 52.7 m/s2 * (1.41 s)2 = 52.3 meters

Now, the velocity at the end of the powered ascent can be found using the equation v = u + at, giving us v = 0 m/s + 52.7 m/s2 * 1.41 s = 74.3 m/s. This is the initial velocity for the free-fall ascent.

For the free-fall, the only acceleration is due to gravity, which is -9.81 m/s2 (negative as it opposes the initial velocity). We use v2 = u2 + 2as to find the additional altitude gained in free-fall when the velocity reaches zero (v = 0 m/s at the maximum height). Solving for 's', we get:

s = (0 m/s)2 - (74.3 m/s)2 / (2 * -9.81 m/s2) = 281.9 meters

So, the total maximum altitude is the sum of the displacement during the powered ascent and the additional altitude gained in free-fall which is 52.3 meters + 281.9 meters = 334.2 meters.

To find the total time elapsed until the rocket strikes the ground, we'll add the time of ascent, the time to reach maximum altitude during free-fall, and the time it takes to fall back down from that altitude. We've already found the time of ascent (1.41 s) and can use the same velocity and acceleration to find the time to reach maximum altitude during free-fall with the formula t = (v - u) / a, giving us t = (0 m/s - 74.3 m/s) / -9.81 m/s2 = 7.57 s. For the descent, the time from maximum altitude to the ground will be equal to twice the time from the end of powered ascent to maximum altitude, since the paths are the same and the final velocities (at the ground) will be equal in magnitude but opposite in direction.

The total time elapsed from takeoff until the rocket strikes the ground is then 1.41 s + 2 * 7.57 s = 16.55 seconds.

Ans: 8 hours and 90 minutes

The length of Football field = 300ft by 160 ft.

On converting it into meter, we get length of field = 91.44 m

and the width of field = 48.8 m 

Now, distance = Area moved/ width = (91.44*48.8) / 0.5 = 8924.55 m = 8.9245 km

Ans, Time taken = distance*speed = 8.9245*1 km/hr = 8 hours and 90 minutes

It would take approximately 8.96 hours for one person to mow a football field with a lawn mower that has a 0.5 meter width and moves at a speed of 1 km/hr.

To estimate how long it would take one person to mow a football field using an ordinary home lawn mower, let's look at the size of an American football field and the capacity of a standard lawn mower. An American football field is 100 yards long, not including the end zones. Since 1 yard is approximately 0.9144 meters, the length of the field is about 91.44 meters. The width of a football field is 53.3 yards, which is about 48.77 meters.

Now, considering the mower has a 0.5 meter width and moves with a speed of 1 km/hour, which equals 0.2778 meters/second (since 1 km/h equals 0.2778 m/s), it is referred to when doing calculations for velocity or speed, we need to convert the dimensions and the speed to compatible units.

The area of the football field can be calculated as 91.44 meters in length multiplied by 48.77 meters in width, resulting in approximately 4460.09 square meters. Now, we will find out how many strips of 0.5 meter width are needed to cover the width of the field: 48.77 meters / 0.5 meters = 97.54, which we round up to 98 passes. Since each pass covers a length of 91.44 meters, a single pass would take 91.44 meters / 0.2778 meters/second = 329.25 seconds. Multiplying this by the number of passes gives us the time to mow the entire field: 329.25 seconds/pass × 98 passes = 32,266.5 seconds, or approximately 8.96 hours.

Newton’s second law states that force is the product of mass and acceleration. This is expressed mathematically as:

F = m * a

Where F = force, m = mass, a = acceleration

Since in the given problem, the force is constant or same force is acting upon two objects. Therefore we can simply equate the expression m * a of the 2 objects.

m1 * a1 = m2 * a2

Where m1 = 2 kg, a1 = 38 m/s^2, m2 = 19 kg. Therefore finding for a2:

2 kg * 38 m/s^2 = 19 kg * a2

a2 = 4 m/s^2     (ANSWER)

We can determine the object with more mass by applying equal force to both objects, the more massive object will accelerate less.

According to Newton's second law of motion, the force applied to an object is directly proportional to the product of the mass and acceleration of the object.

F = ma

[tex]a = \frac{F}{m}[/tex]

where;

At equal force, the object with less mass will accelerate more.

Thus, we can determine the object with more mass by applying equal force to both objects, the more massive object will accelerate less.

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Answer:

Find an activity you enjoy and make it a priority in your schedule

Explanation:

Final answer:

The neutral load demand for a 25 kW electric range may be considered negligible or zero for calculations unless the manufacturer's documentation indicates otherwise, due to typically being a pure 240V appliance with balanced legs.

Explanation:

The neutral load demand for an electric range rated at 25 kW will depend on whether the range is designed for a balanced three-phase power supply or a single-phase power supply. In a residential setting in the United States, it is typically single-phase. For many electric ranges, the neutral only carries the imbalance current, which is the difference between the two hot legs of a 240V circuit. However, if the range uses 120V components such as lights or controls, the neutral would carry that load as well. If we assume a pure 240V appliance with no 120V components and perfect balance, there would be no current on the neutral. In practice, there might be some load on the neutral, but for the purpose of this question and the majority of calculations for residential service, we often consider it to be negligible or zero for a large 240V appliance like a 25 kW range, unless specified by the manufacturer's documentation.

An artesian well is a well drilled into an artesian aquifer. An artesian aquifer is a small aquifer which contains groundwater under positive pressure. Since the water is under positive pressure, this forces the water level in the well to rise above the water surface up to a point where hydrostatic equilibrium is reached. This results in the formations of “Springs”.

Answer: Spring 

Final answer:

An artesian well can create a spring when the pressure is sufficient to allow water to flow to the surface. This event has the potential to affect the local water table and contribute to larger water management challenges such as saltwater intrusion and subsidence.

Explanation:

When an artesian well begins to push out enough water that gravity causes it to flow to a lower region, a spring is formed. This occurs when the pressure within the confined aquifer becomes greater than the pressure exerted by the atmosphere above it, allowing the groundwater to flow out without the need for pumping. If the water finds its way to the surface, it can emerge as a spring and potentially form a stream, depending on the topography and geology of the area.

The creation of a spring due to the development of an artesian well may alter the local water table and potentially reduce the volume of water in other nearby wells or surface water bodies. Associated issues such as groundwater mining, saltwater intrusion, and damage through subsidence and sinkholes can arise if the water extraction is not managed sustainably, contributing to the broader context of a water supply crisis.

The answer is the universe. It can be defined as everything that exists, everything that has occurred, and everything that will exist.  It is also all of space and time and its contents which comprises of moons, planets, minor planets, stars, galaxies, the contents of intergalactic space and all matter and forms of energy (including electromagnetic radiation and matter), and the physical laws that relate them. The Universe covers all of life, all of history, and some theorists and scientists recommend that it even encompasses notions such as logic and mathematics.

Final answer:

The universe is the totality of all space, time, matter, and energy. In physics, the study of energy, matter, space, and time falls under the field of physics. It explores concepts such as gravity, electromagnetism, strong and weak nuclear forces that govern the behavior of matter and energy in the universe.

Explanation:

The universe is the totality of all space, time, matter, and energy.

In physics, the study of energy, matter, space, and time falls under the field of physics. It is concerned with describing the interactions between these fundamental components and understanding the mechanisms that underlie every phenomenon.

For example, physics explores concepts such as gravity, electromagnetism, strong and weak nuclear forces that govern the behavior of matter and energy in the universe.

Question one the answer is 339 kj

Question two the answer is 9.02 kj

Question three - No

In order to free your vessel when you run aground in an outboard boat and you are not taking on the water, the very first thing you need to do is just to stop the boat’s engine to stop it from moving then try to lift the out drive, and shift the weight away from the impact zone.  Once this is done, you can already now assist the situation and you will be sure that the bat will no longer take into the water.  You can now set an anchor in order for you to be safe from the force that can push you and the boat further.  You can then use the boat hook so you can check how deep the water is around you.

If you run aground in an outboard boat and you are not taking on water, the first step in attempting to free your vessel is to stop the engine and then lift it.

A gasoline engine refers to a mechanical system that is designed and developed to use hydrocarbons such as fuels, in order to enable a vehicle or boat to move from one point to another on a water surface.

In Engineering, an outboard gasoline engine is typically installed on the outside of a vehicle or transport system such as a boat, rather than in its interior.

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Final answer:

The magnetic force on a stationary charged particle is zero, while the magnetic force on a moving charged particle is non-zero. When charges are stationary, their electric fields do not affect magnets. However, when charges move, they produce magnetic fields that exert forces on other magnets.

Explanation:

The magnetic force on a stationary charged particle is zero, while the magnetic force on a moving charged particle is non-zero. When charges are stationary, their electric fields do not affect magnets. However, when charges move, they produce magnetic fields that exert forces on other magnets. The magnitude of the magnetic force on a charge q moving at a speed v in a magnetic field of strength B is given by F = quB sin θ.

Answer: A. How the soil particles clump together

Explanation:

Solid part of the soil clumps together. There are air pores between the soil particles. This determines the soil structure. The soil takes the shape based on the its physical and chemical properties. The main four types of soil structure are:  

1. Columns

2. Blocky

3. Granular

4. Plate-like

The fastest way to reach maximum braking capability, whether with or without ABS, is to firmly and rapidly apply the brakes. If the car has an ABS, the system would automatically prevent the wheels from locking up, but without it, the driver should manually pump the brakes.

The fastest way to reach maximum braking capability, whether your vehicle contains the Anti-lock Braking System (ABS) or not, is to blast the brakes. This method is about firmly and rapidly applying the brake pedal. With ABS, the system takes over and prevents the wheels from locking up, while without ABS, the driver should pump the brakes to avoid wheel lock up. However, keep in mind that in both cases, keep your steering wheel steady and do not turn it abruptly.

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The fastest way to reach maximum braking capability is to apply the brakes as hard as possible without locking up the wheels, either manually or with ABS.

The fastest way to reach maximum braking capability with or without ABS is to apply the brakes as hard as possible without locking up the wheels. This creates the maximum friction between the tires and the road, allowing the vehicle to decelerate quickly.

With ABS (Anti-lock Braking System), the braking system automatically modulates the brake pressure to prevent wheel lock-up, ensuring that the tires remain in contact with the road and maximizing braking efficiency.

Without ABS, the driver needs to manually pump the brakes to prevent wheel lock-up. This allows the tires to maintain traction and achieve maximum braking capability.

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Final answer:

To excel at volleyball, Doug should focus intently on deliberate practice of jumping, speed, agility, endurance, and hand-eye coordination, backed by continuous assessment and technique improvement.

Explanation:

Doug wants to excel at volleyball and has listed a set of skills to improve on, including jumping, speed, agility, endurance, and hand-eye coordination. To truly excel, Doug should focus on deliberate practice in these areas as it is the key to success in athletic events according to studies by Anders Ericsson. Additionally, an internal and external focus on physical performance, as studied by Gabrielle Wulf and colleagues, can enhance outcomes related to balance, accuracy, speed, and endurance, which are essential for volleyball. Doug should assess his current skill levels, identify specific ways to improve, and engage in intensive practice and mental agility exercises to improve his volleyball performance.

D: Neither ultrasonic nor infrasonic vibrations can be heard by humans.

Answer

D. Neither ultrasonic nor infrasonic vibrations can be heard by humans.

Explanation

Human hearing is somehow limited. Frequencies below 20 Hz cannot be heard by human and sounds of frequencies above 20,000 Hz too. The sounds of frequency below 20 Hz are known as the infrasonic sounds. Those above 20,000 Hz are called Ultrasonic sounds.

The volume of the mercury sample is approximately 4.28 × 10⁻⁶ m³.

To find the volume of the mercury sample, we can use the formula: density = mass/volume. Rearranging the formula, we have volume = mass/density. The weight of the sample is 6.0 N, and with the acceleration due to gravity being 9.81 m/s², we can calculate the mass of the sample using the formula weight = mass × acceleration due to gravity. Therefore, mass = weight/acceleration due to gravity. Plugging in the values, we get mass = 6.0 N/(9.81 m/s²).

Next, we substitute the calculated mass and the given density into the formula to find the volume: volume = mass/density. With the calculated mass and the given density of 13.6 × 10³ kg/m³, we get volume = mass/density = (6.0 N/(9.81 m/s²))/(13.6 × 10³ kg/m³).

Simplifying the expression, the volume of the sample is approximately 4.28 × 10⁻⁶ m³.

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if it travels at 50km in 1 hour

 than it would travel 50 x 1/2 for a half an hour

50 * 1/2 = 25km

Pamela can drive 121,333,212 kilometers with 121212 liters of fuel, given her car's fuel efficiency is 1001 kilometers per liter.

Pamela drove her car 999999 kilometers using 999 liters of fuel. She wants to know how many kilometers (k) she can drive with 121212 liters of fuel, assuming the relationship between kilometers and fuel is proportional.

To find the number of kilometers she can drive with 121212 liters of fuel, we first need to determine her car's fuel efficiency, which is:

Fuel Efficiency (km per liter) = 999999 km / 999 liters = 1001 km per liter

Next, we use this fuel efficiency to calculate the distance she can drive with 121212 liters of fuel:

Distance (k) = Fuel Efficiency × Amount of Fuel

Distance (k) = 1001 km per liter × 121212 liters = 121333212 kilometers

Therefore, Pamela can drive 121,333,212 kilometers with 121212 liters of fuel.