Two planets have the same surface gravity, but planet b has twice the radius of planet
a. if planet a has mass m, what is the mass of planet b?

We must take note that the 28 meters high is simply a diversion. What we only need is the 4 hours and 12 kilometers distance. The formula for calculating the speed or velocity is :

velocity = distance / time

Therefore:

velocity = 12 km / 4 h

velocity = 3 km / h = 0.83 m / s 

Answer: So the campers must travel 12km two times (because they must go back after reached the lighthouse), and 28m two times.

If they keep the velocity constant (it means that they climb up and down the stairs at the same speed that they walk )

then you could add the whole distance as 12km*2 + 28m*2

a km is 1000m, so the distance will be 12000*2m+28*2m = 24046m

and they have 4 hours to do this, so the velocity is distance over time, they should do 24046m/4hours = 6011.5m/h or 6.0115km/h

Final answer:

The speed mentioned is approximately half the escape velocity from Earth and is not sufficient to escape Earth's gravitational field. The object will ascend to a maximum altitude before falling back down. A specific calculation would require further application of physics principles.

Explanation:

The question is related to the concept of escape velocity in physics, which is the speed needed to break free from a planet's gravitational pull without further propulsion. The escape velocity from the surface of the Earth is approximately 11 km/s. At a speed of 5534 m/s, which is approximately 5.5 km/s (half the escape velocity), the object will not have enough kinetic energy to completely escape Earth's gravity and hence will reach a maximum altitude before falling back to Earth. To calculate precisely how far from the center of the Earth you would get with the initial speed of 5534 m/s, you would need to use the equations for gravitational potential energy and kinetic energy, considering how much kinetic energy converts into potential energy as the object ascends against Earth's gravity.

both a and b

ur answer is d

The beanbag was thrown in a motion with an initial velocity of 10.78 m/s and reached a peak height of 5.929m.

The height and initial velocity of a thrown object can be calculated using kinematics, a branch of physics that describes motion of objects. Since the beanbag is thrown up and comes back to the same spot, the total time of its flight (2.2s) is split between the time going up and the time coming back down.

We can simplify calculations by assuming that the time for the journey upwards equals the time for the journey downwards, i.e., 1.1s each.

The highest point is reached when the velocity is zero. We can use the formula v= u + at to find the initial velocity (u), where v is the final velocity, a is acceleration due to gravity (-9.8m/s² due to the upward direction), and t is the time (1.1s). For the highest point, we can use the formula h = ut + 0.5at².

Calculating this, we find the initial velocity u = -9.8 × 1.1 = -10.78 m/s (it's negative because we took upward direction as negative). To calculate the highest point or maximum height, we find h = -10.78 × 1.1 + 0.5 ×  -9.8 × (1.1)² = -5.929 m (this is also negative due to upward direction). Hence, the beanbag was thrown up with an initial velocity of 10.78 m/s and reached a maximum height of 5.929 m.

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Final answer:

Using the density of pure silver (10.5 g/cm³), we calculate that 5.25 g of silver will have a volume of 0.5 cm³, raising the water level in the graduated cylinder from 11.2 mL to 11.7 mL.

Explanation:

The question asks to determine the volume level rise in a graduated cylinder when 5.25 g of pure silver is added to it. To find the rise in the volume of water within the cylinder, we utilize the concept of density, which relationship between mass and volume of a substance. The density of pure silver is given as 10.5 g/cm3. We can calculate the volume of the silver using the formula: Density = Mass / Volume, hence Volume = Mass / Density. Substituting the given values, we get Volume = 5.25 g / 10.5 g/cm3 = 0.5 cm3. Therefore, the volume level in the graduated cylinder will rise from 11.2 mL to 11.7 mL (since 1 cm3 = 1 mL).

The equation of motion that we can use in this case is:

t = d / v

where t is time, d is distance, v is velocity

Therefore calculating for t:

t = 3.5 km / (25 km / h)

t = 0.14 h = 8.4 minutes

It takes approximately 8.4 minutes for a bird flying at 25 km/h to cover a distance of 3.5 km.

To determine how long it takes for a bird to fly 3.5 km at a speed of 25 km/h, we can use the formula for time, which is distance divided by speed. The calculation is as follows:

Time = Distance / Speed

Time = 3.5 km / 25 km/h = 0.14 h

To convert hours to minutes, multiply by 60:

Time = 0.14 h × 60 minutes/h = 8.4 minutes

Thus, it will take the bird approximately 8.4 minutes to fly 3.5km.

Final answer:

The Earth rotates at an angular velocity of 15 degrees per hour. Without specific flight path distances, we refer to Earth's rotation speed as a base reference for understanding angular velocity in a general sense.

Explanation:

The flight from Kampala to Singapore takes 7.0 hours. To calculate the plane's angular velocity relative to the Earth's surface, we need to understand that completing a flight between two points on Earth's surface involves moving over a certain segment of Earth's rotation. Since the Earth completes one full rotation (360 degrees) in 24 hours, we can calculate the angular velocity (in degrees per hour) by simply dividing the total degrees by the total hours.

Angular velocity = Total rotation / Time = 360 degrees / 24 hours = 15 degrees per hour.

However, this is the angular velocity of the Earth itself. A plane's angular velocity relative to Earth would depend on the distance traveled. But without specific details on the distance covered, we can only refer to the Earth's own rotation speed as a base reference, which is 15 degrees per hour. For a specific flight, beyond this basic understanding, actual calculation would require details about the exact flight path length over the Earth's surface.

The force acting on a body is directly proportional to both mass and acceleration. Hence, the an increase in acceleration with a smaller mass does not make an increase  in force than that act on a larger mass with less acceleration. Hence, the net force will be the same for both masses.

Force is an external agent acting on a body to deform it or to change its state of motion or rest.  Force is a vector quantity thus, it is characterized by a magnitude and direction.

The force according to second law of motion is the product of mass and acceleration of the body. Hence, an increase in mass or acceleration or both  results in an increase in force.

Here, the force F1 is acting on the mass 3 Kg with an acceleration of 2a

and force F2 is acting on 6 Kg with an acceleration a.

Then F1  = 3 × 2 a = 6a

F2 = 6 × a = 6a.

Thus, net force of both are equal.

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True, the greater the mass of an object, the greater its force due to gravity.

The force due to gravity on object's is calculated by applying Newton's second law of motion as follows;

F = mg

where;

From the formula given above we can conclude that, the greater the mass of an object, the greater its force due to gravity.

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The statement addresses Isaac Newton's law of gravitation which suggests that the greater the mass of an object, the greater its force due to gravity. Gravitational attraction is a universal property of mass. Mass is constant while weight varies with the gravitational field strength.

The statement in question - 'The greater the mass of an object, the greater its force due to gravity' - is a fundamental principle in Physics, specifically in the study of gravity. Gravity is essentially a 'built-in' property of mass, meaning all masses in the universe interact via the force of gravitational attraction. The British physicist Sir Isaac Newton concluded that the gravitational attraction between two bodies is proportional to their masses and inversely proportional to the square of the distance between them. This is illustrated in Newton's law of gravitation, formulated as Fgravity = G × (M1 × M2) / R².

It's important to note also that the weight of an object, which is the force of gravity acting on it, varies with the strength of the gravitational field. Mass, however, is a constant property of an object and does not change regardless of the gravity acting on it. Mass is a measure of the amount of matter in an object, whereas weight is the gravitational pull acting on that matter.

Understanding these principles allows us calculate the masses of astronomical objects and understand a range of natural phenomena, from the motion of a falling apple to the orbits of planets.

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Final answer:

To find the upward thrust force needed to accelerate the rocket, we use Newton's second law of motion. The upward thrust force needed is approximately 4989.2 N.

Explanation:

To find the upward thrust force needed to accelerate the rocket, we can use Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, the mass of the rocket is 590 kg and the acceleration is the change in velocity divided by the time taken.

Using the formula acceleration = (final velocity - initial velocity) / time, we can calculate the acceleration:

acceleration = (28 m/s - 0 m/s) / 3.3 s =  8.48 m/s²

Now that we have the acceleration, we can calculate the upward thrust force:

force = mass x acceleration = 590 kg x 8.48 m/s² = 4989.2 N

Therefore, the upward thrust force needed to accelerate the rocket uniformly to an upward speed of 28 m/s in 3.3 s is approximately 4989.2 N.

To accelerate the 590-kg rocket uniformly to an upward speed of 28 m/s in 3.3 s, a thrust force of approximately 5010.2 N is required, calculated using Newton's second law.

To determine the upward thrust force needed to accelerate the rocket uniformly, we can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

First, calculate the acceleration (a) of the rocket using the kinematic equation:

v = u + at

where:

v is the final velocity (28 m/s),

u is the initial velocity (0 m/s, as the rocket is at rest),

a is the acceleration, and

t is the time (3.3 s).

Rearrange the equation to solve for acceleration:

a = (v - u) / t

Substitute the values:

a = (28 m/s - 0) / 3.3 s ≈ 8.48 m/s^2

Now, use Newton's second law to find the force (F):

F = ma

F = 590 kg × 8.48 m/s^2 ≈ 5010.2 N

The mass of the chain in two decimal places is 2.55 kg.

The tension at the end of the chain is due to the weight of the weight supported by the chain.

The mass of the chain is calculated by applying Newton's second law of motion as follows;

W = mg

where;

m = W / g

The mass of the chain is calculated as;

m = ( 25 N ) / ( 9.8 m/s² )

m = 2.55 kg

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The mass of the chain can be calculated using the formula Mass = tension / gravity. Given the values for tension and gravity, the mass of the chain is approximately 2.55 kg.

This is a problem related to the physics concept of force, mass, and acceleration due to gravity. Since we know that the tension in the chain isn't affected by the chain's length, we can assume that the tension is evenly distributed along the chain, with 25 N at each end.

The tension in the chain is equal to the weight of the chain. Therefore, we can use the formula for calculating the weight, which is Weight = mass x gravity. Since we know that the weight is equal to the tension, we can solve the formula for mass, which gives us Mass = tension / gravity. Substituting the given values, we have: Mass = 25 N / 9.8 m/s² = 2.55 kg.

Therefore, the mass of the chain is approximately 2.55 kg.

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Let us say that:

1 = 1st player notation

2 = 2nd player notation (the opponent)

a. First let us establish the distance travelled by the 2nd player:

d2 = 13 m/s * (t + 1.5)

d2 = 13 t + 19.5

Then the distance of the 1st player:

d1 = v0 t + 0.5 a t^2         (v0 initial velocity = 0 since he started from rest)

d1 = 0.5 * 4 m/s^2 * t^2

d1 = 2 t^2

The two distances must be equal, d1 = d2:

2 t^2 = 13 t + 19.5

t^2 – 6.5 t = 9.75

Completing the square:

(t – 3.25)^2 = 9.75 + (- 3.25)^2

t – 3.25 = ±4.5

t = -1.25, 7.75

Since time cannot be negative, therefore:

t = 7.75 seconds

So he catches his opponent after 7.75 seconds.

b. Using the equation:

d1 = 2 t^2

d1 = 2 * (7.75)^2

d1 = 120.125 m

So he travelled about 120.125 meters when he catches up to his opponent.

It takes 3.25 seconds for the first player to catch the opponent. The first player has traveled 21.125 meters when they catch the opponent.

Given:

Opponent's speed (v₁) = 13 m/s

Acceleration of the first player (a) = 4.0 m/s²

Time (t) = 1.5 s

(a) We can use the following equation:

v = u + at

13  = 0 + 4.0 × t

t = 13 / 4.0

t = 3.25 s

Therefore, it takes 3.25 seconds for the first player to catch the opponent.

(b) we can use the equation:

s = ut + (1/2)at²

s = 0 × 3.25 + (1/2) × 4.0 × (3.25 )²

s = 0 + (1/2) × 4.0 × 10.5625

s = (1/2) × 4.0 × 10.5625

s = 21.125 m

Therefore, the first player has traveled 21.125 meters when they catch the opponent.

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Those stitches are what "chews" into the wind when you like to throw a breaking ball. Additionally, a knuckleball that barely spins eats at the wind using the stitches on the ball and this enables it to drop, sail or rise.

In short, the stitches makes the ball air resistant or cut into air making it faster.

The most ‘striking’ feature of the baseball is the stitches that interact with the air when the ball moves. Along with a slight effect on the air drag, there is a strong effect on the Magnus force. According to the stitch pattern, the Magnus force on a moving ball depends accordingly because the air interacts strongly with the raised stitches on the ball. Apart from this, the stitches provide a better grip for the pitcher and help in forcing the ball to move in different ways.

Final answer:

The question delves into historical instances of execution by hanging, touching on both real individuals like John Brown and Nat Turner, and fictional characters such as Peyton Farquhar. These figures were tied to pivotal societal and political issues, such as slavery and civil war, facing harsh penalties for their actions.

Explanation:

The question refers to various historical figures who were executed by hanging for their actions which often had considerable political or social impact. Peyton Farquhar, a fictional character from Ambrose Bierce’s short story, "An Occurrence at Owl Creek Bridge", symbolizes the concept of civilian interference in military matters and the grim consequences that follow during times of war. He is described as a genteel man, suggesting that civil status did not exempt one from capital punishment. A reference is made to John Brown, a historical figure who was hanged in 1859 after attempting to initiate a slave revolt at Harpers Ferry, effectively marking a critical moment that stirred greater national tension leading to the American Civil War.

Similarly, it mentions Nat Turner, leader of a slave rebellion in Virginia, which led to a swift and brutal response from the state authorities and white vigilantes, resulting in his death along with many other Black individuals, free and enslaved. Lastly, it hints at the Fugitive Slave Law and the repercussions for those who attempted to help enslaved individuals escape, as in the case of the unidentified 'young white man from Ohio.' This aligns with historical accounts of abolitionists and their often fatal attempts to combat slavery.

The net force acting on the refrigerator is 400 N to the right

[tex]\texttt{ }[/tex]

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

mass of refrigerator = m = 200 kg

magnitude of applied force = F = 400 N

magnitude of frictional force = f = 0 N

Asked:

net force = ΣF = ?

Solution:

We will use Newton's Law of Motion to solve this problem as follows:

[tex]\Sigma F = F - f[/tex]

[tex]\Sigma F = 400 - 0[/tex]

[tex]\boxed{\Sigma F = 400 \texttt{ N} }[/tex]

[tex]\texttt{ }[/tex]

We could also calculate the acceleration of the refrigerator as follows:

[tex]\Sigma F = ma[/tex]

[tex]a = \Sigma F \div m[/tex]

[tex]a = 400 \div 200[/tex]

[tex]\boxed{a = 2 \texttt{ m/s}^2 }[/tex]

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Dynamics

To find the density of a cylinder, its volume is first determined using the formula V = πr²h. After correcting the radius and height according to the question, the density is calculated as mass divided by volume, approximately 6.65 g/cm³. Compared to standard material densities, the cylinder may be made of a type of stainless steel or a similar metal alloy.

To calculate the density of the cylinder, we first need to find its volume using the formula V = πr²h. Given that the length (height) is 3.23 cm and the diameter is 1.75 cm, the radius (r) would be half of the diameter, which is 0.875 cm. However, there seems to be a typo or mistake in the provided sample work as it uses a radius of 0.750 cm and a height of 5.25 cm, which do not match the question's parameters. Assuming the correct measurements, we would use:

V = π × (0.875 cm)² × 3.23 cm = 9.818 cm³

Now, to find the density, we divide the mass by the volume:

Density = Mass / Volume = 65.3 g / 9.818 cm³ = 6.65 g/cm³

Based on common material densities, this cylinder could potentially be made of stainless steel which typically has a density around 8 g/cm³; however, since our calculated density is slightly less, it could be a stainless steel alloy or a similar metal with a slightly lower density.

Final answer:

To determine the initial speed of the second arrow when both arrows reach their maximum height at the same time, kinematic equations are utilized, taking into account the initial velocity of the first arrow, delay time before the second arrow is fired, and gravity's acceleration.

Explanation:

The problem given is a classic example of two-body motion in which two arrows are launched vertically with different initial velocities, and the challenge is to find the initial speed of the second arrow when both arrows reach their peak heights simultaneously. To solve this problem, we need to use the equations of kinematics for each arrow.

First, we find the time it takes for the first arrow to reach its maximum height using the initial speed and the acceleration due to gravity. The equation for this is derived from the kinematic equation v = u + at, where v is the final velocity (0 m/s at maximum height), u is the initial velocity (31.8 m/s), a is the acceleration (-9.8 m/s² directed downwards), and t is the time. Thus, the time, t, for the first arrow to reach its maximum height can be calculated as follows:

t = (v - u) / a

Knowing the time it takes for the first arrow to reach the maximum height, we can then calculate the initial speed of the second arrow, which is fired 1.82 s later. This involves adding the delay time to the time it took the first arrow to reach the maximum height and then using that total time to determine the initial speed of the second arrow using the kinematic equation u = v - at, with v again being 0 m/s at maximum height.

By carefully evaluating these kinematic equations, we find the initial speed of the second arrow, ensuring that both arrows reach their peak heights at the same moment.

Final answer:

SI base units are the seven fundamental units in the SI system, such as kilograms for mass; derived units, such as grams per milliliter for density, are constructed by combining base units. Derived units are essential for expressing a wide range of physical quantities, demonstrating the SI system's adaptability.

Explanation:

The difference between SI base units and derived units lies in their definitions and applications. SI base units are the seven fundamental units of measurement in the International System of Units (SI) that are defined by specific physical phenomena and are independent of each other. These include the kilogram (kg) for mass and the meter (m) for length, among others. On the other hand, derived units are units that are constructed by combining the base units according to algebraic relationships. Examples of derived units include grams per milliliter (g/mL) for density and joules (J) for energy, which are obtained by combining base units in multiplicative ways.

Derived units can express a wide variety of physical quantities such as area, volume, density, and energy, showcasing the versatility of the SI system. Combining prefixes with base units can also create new units of larger or smaller sizes, enhancing the adaptability of the system to cover a broad range of measurements from the microscopic to the astronomical scale.