A train is slowing down with an average acceleration of −5.0 m/s2 (negative sign shows deceleration). If its initial velocity is 50. m/s, how far does it travel in 6.0 seconds?

In the vertical direction there is no change of momentum.

Momentum in vertical = 1.5 * 9 = 13.5
Speed in vertical = 9 m/s
Momentum of Raven in x + momentum of falcon = initial momentum in x
=> Mx + 600*5 = 600*20
=> Mx = 600*15
=> Vx = 6000

Vy = 9

=> tanθ = 0.6 kg/9 = 0.066667

=> θ = 48.0128 degrees

The angle of raven changes to [tex]\boxed{48.01^\circ}[/tex]  from initial direction after impact.

Further Explanation:

A collision is a phenomenon where, two or more object exerts forces on each other or colloid each other in comparatively short time.

An elastic collision is a collision where, after collision the net kinetic energy of the body remains constant. The kinetic energy and momentum is always conserved in the elastic collision.

An inelastic collision is a collision where, after collision the net kinetic energy of the body does not remain constant. The momentum is always conserved but the net kinetic energy does not conserve in an inelastic collision.

Given:

The mass of the is [tex]600\text{ g}[/tex].

Mass of the raven is [tex]1.5\text{ kg}[/tex].

Velocity of the falcon is [tex]20.0\text{ m/s}[/tex].

Velocity of the raven is [tex]9.00\text{ m/s}[/tex].

Concept:

Here the two birds undergo an elastic collision.

During impact the falcon strikes the raven at right angle and after impact the falcon bounce back as shown in the Figure 1.

Before impact the falcon moving towards positive y-axis direction and the raven is flying towards positive x-axis direction and after impact the falcon flying toward the negative y-axis direction.

Apply conservation of linear momentum.

[tex]\fbox{\begin\\{m_1}{\vec v_1} + {m_2}{\vec v_2}={m_1}{\vec v_1}^\prime  + {m_2}{\vec v_2}^\prime\end{minispace}}[/tex]

Here, [tex]{m_1}[/tex] is the mass of the falcon; [tex]{v_1}[/tex] is the velocity of falcon, [tex]{m_2}[/tex] is the mass of the raven, [tex]{v_2}}[/tex] is the velocity of raven, [tex]{v_1}^\prime[/tex] is the velocity of falcon after collision and [tex]{v_2}^\prime[/tex] is the velocity of raven after collision.

Substitute for [tex]600\text{ g}[/tex] for [tex]{m_1}[/tex], [tex]20.0\text{ m/s}[/tex] for [tex]{v_1}[/tex], [tex]1.5\text{ kg}[/tex] for[tex]{m_2}[/tex], [tex]9.00\text{ m/s}[/tex] for [tex]{v_2}[/tex] and [tex]5.00\text{ m/s}[/tex] for [tex]{v_1}^\prime[/tex] in the above equation.

[tex]\left( {600{\text{ g}}\left( {\frac{{1{\text{ kg}}}}{{1000{\text{ g}}}}} \right)} \right)\left( {20.0{\text{ m/s }}\hat j} \right) + \left( {1.5{\text{ kg}}} \right)\left( {9.00{\text{ m/s }}\hat i} \right) = \left( {600{\text{ g}}\left( {\frac{{1{\text{ kg}}}}{{1000{\text{ g}}}}} \right)} \right)\left( {5.00{\text{ m/s}}\left( { - {\text{ }}\hat j} \right)} \right) + \left( {1.5{\text{ kg}}} \right){v_2}^\prime[/tex]

Simplify further.

[tex]{v_2}^\prime=9{\text{ m/s }}\hat i + 10{\text{ m/s }}\hat j[/tex]

The magnitude and the angle of raven after impact is given by:

[tex]\begin{aligned}{v_2}^\prime&=\sqrt {{{10}^2} + {9^2}} {\text{ m/s}}\angle{\tan ^{ - 1}}\left({\frac{{10}}{9}} \right)\\ &=\sqrt {181} {\text{ m/s}}\angle 48.01^\circ\\&=13.45{\text{ m/s}}\angle 48.01^\circ\\ \end{aligned}[/tex]

Therefore, the angle of raven changes to [tex]\boxed{48.01^\circ}[/tex]  from initial direction after impact.

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Answer Details:

Grade: High school

Subject: Physics

Chapter: Kinematics

Keywords:

Protecting, his, nest, 600 g, peregrine, falcon, rams, marauding, 1.5 kg, raven, moving, 20.0 m/s, 9.00 m/s, moment, impact, strikes, right angle, direction, rebounds, straight, back, 5.00 m/s, angle, 48.01 deg, 13.45 m/s.

When Mars and Earth are on opposite sides of the sun, the distance between them is approximately 4.0x108 km. Given that the speed of light is about 3.00x105 km/s, it takes just over 22 minutes (or around 1333.33 seconds) for a radio signal to travel from Earth to Mars.

The speed of light, denoted as c, is approximately 3.00 x 105 km/s. We are given that the distance between Mars and Earth when they are on opposite sides of the Sun is approximately 4.0 x 108 km. Since speed is defined as the distance traveled per unit of time, we can calculate the time it takes for a radio signal to travel from Earth to Mars by dividing the total distance by the speed of light.

Using the formula Time = Distance/Speed, replacing the symbols with the values given results in: Time = 4.0x108 km / 3.00x105 km/s. Performing the calculation reveals that it takes approximately 1333.33 seconds for a radio signal to travel from Earth to Mars when they are on opposite sides of the sun.

This answer tells us that even at the speed of light, interplanetary communication experiences considerable delays due to the vast distances involved. For instance, if astronauts on Mars were trying to communicate with their counterparts on Earth, there would be a delay of just over 22 minutes each way.

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The Mack truck has the higher force of impact, Mini cooper has the greater impulse, greater change in momentum occurs in Mini cooper, and the Mack truck has greater deceleration.

A characteristic of a moving body that it possesses due to its mass and motion and is equal to the sum of its mass and speed. Momentum is a vector quantity, which means it has magnitude with direction.

Due to its size and higher center of gravity, the Mack truck would impact with a larger force. Since a tiny cooper is lighter and smaller than a Mack truck, it would have a higher impulse. Due to its lesser weight and the fact that the Mack truck's impact would exert more force on it, the mini cooper would also experience a bigger change in momentum.

Due to its greater weight and longer slow down time, the Mack truck would experience a greater deceleration.

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Final answer:

To find the mass of a lead cube with the same dimensions as an iron cube weighing 250 g, calculate the volume of the iron cube and multiply it by the density of lead, resulting in a mass of 359.01 g for the lead cube.

Explanation:

The mass of the iron cube is given as 250 g with a density of 7.87 g/cm³. To find the mass of a lead cube with the same dimensions, we first need to calculate its volume, then multiply it by lead's density to determine its mass. Using the provided density of lead (11.3 g/cm3), the calculation is as follows:

Volume of the iron cube = Mass / Density = 250 g / 7.87 g/cm³ = 31.77 cm³ (rounded to two decimal places).

Since both cubes have the same volume, the volume of the lead cube is also 31.77 cm³.

Mass of the lead cube = Volume x Density of lead = 31.77 cm³ x 11.3 g/cm³ = 359.01 g (rounded to two decimal places).

The atomic mass of an element provides crucial information about the element, including its identity, its reactions with other elements and its behavior. It is determined by the total number of protons and neutrons. It can give you an idea about the size and weight of an atom.

The atomic mass of an element is determined by the total number of protons and neutrons in an atom's nucleus. It provides crucial information about the element, including its identity, how it reacts with other elements and its behavior. For example, hydrogen has an atomic mass of 1 because it has one proton and no neutrons. On the other hand, helium has an atomic mass of 4, because it has two protons and two neutrons. Therefore, the atomic mass can give you an idea of the size and weight of an atom.

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The correct answer would be "two-thirds"

Final answer:

To find the weight of an object on another planet with 1/10th of Earth's gravity, multiply the mass by the reduced gravitational force (0.98 m/s²) giving a weight of 0.98 N for a 1.0-kg object.

Explanation:

The weight of an object on another planet where gravitational attraction is reduced to 1/10 of Earth's can be calculated by adjusting the gravitational force. On Earth, the acceleration due to gravity, g, is 9.80 m/s², and the weight w of a 1.0-kg object is thus 9.8 N calculated by w = m * g. If the gravitational pull is 1/10th that of Earth's, the acceleration due to gravity on this new planet would be 0.98 m/s². Therefore, the weight of a 1.0-kg object on this planet would be:

w = m * g

= (1.0 kg) * (0.98 m/s²)

= 0.98 N.

So, an object that weighs 9.8 N on Earth would weigh just 0.98 N on a planet where gravity is 1/10 as strong.

Answer: Heterogeneous mixture - the parts are not uniformly mixed.

A mixture contains components having distinct chemical properties. There are two types of mixtures: homogeneous and heterogeneous. In a homogeneous mixture there is uniform distribution of components. we cannot distinguish one portion of the mixture from another. for example salt mixed in water. In heterogeneous mixture, the components are not uniformly mixed. hence, we are able to distinguish different parts of a mixture, like the mixture of iron, sand and salt given in this question.

A protostar, an early stage of stellar evolution, does not always become a star. It depends on the mass of the protostar. Protostars with enough mass become stars by successfully starting nuclear fusion, while those with lower mass may become brown dwarfs.

In the field of Astronomy, a protostar refers to the early stage of stellar evolution, a dense area in a molecular cloud where a star begins to form. Not all protostars successfully become stars. The evolution of a protostar into a star is largely dependent on the mass of the protostar. If the protostar has enough mass, it will continue to condense and heat up until it begins nuclear fusion, and officially becomes a star. If the protostar doesn't have enough mass, it may instead become a brown dwarf - a type of sub-stellar object that is too low in mass to sustain nuclear fusion in its core.

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Not all protostars become stars. Protostars with enough mass ignite nuclear fusion of hydrogen and become main sequence stars, while lower mass protostars that can't sustain hydrogen fusion become brown dwarfs, a category between planets and stars.

In the context of stellar evolution, not all protostars necessarily become stars in the traditional sense. Protostars are essentially young stars in the process of formation, a phase that sees impressive contraction and accumulation of dust and gas from their environment. This process notably generates heat and infrared radiation. However, the endpoint of a protostar's journey relies much on its mass.

If the protostar accretes enough matter to increase its core temperature and trigger nuclear fusion of hydrogen, it successfully becomes a main sequence star which is commonly referred to as a 'star'. In fact, our very own Sun went through this stellar development path. Otherwise, if a protostar lacks sufficient mass to instigate hydrogen fusion, it ends up becoming a 'failed star' known as a brown dwarf. Brown dwarfs are objects that straddle the line between planet and star, with some characteristics of both.

To elaborate, as a protostar collapses under its own gravity, it radiates away its heat, shrinking and becoming denser until its core becomes hot enough to trigger nuclear fusion, turning hydrogen into helium. If the mass is there, this fusion process will continue, and a star is born. If the mass isn't sufficient, nuclear fusion won't occur and thus, a brown dwarf is formed.

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The rock had potential energy as it rested on the edge of the cliff, and it had kinetic energy as it descended toward the earth, kinetic energy is increasing and setting it in motion.

Potential energy is a type of stored energy that depends on how various system elements interact with one another. A spring's potential energy increases when it is squeezed or stretched, for instance. A steel ball has higher potential energy if it is lifted above the ground as opposed to falling to the ground.

Kinetic energy is the energy that an object has as a result of motion. To accelerate an object, a force must be supplied to it. To apply a force, we must exert effort. Energy is transmitted to the object once the work is accomplished, at which point it moves at a new, constant speed.

Boulder when accelerates towards the ground then the kinetic energy will increase as it potential energy is decreasing and velocity is increasing.

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Temperature affect water potential. Water will diffuse down gradients of water potential, just as heat will flow down gradients of temperature and rocks will roll down gradients of gravitational potential.

Gravitational potential energy is energy an object possesses because of its position in a gravitational field. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s².

The potential energy of water per unit volume in comparison to pure water under reference conditions is known as water potential. The tendency of water to migrate from one place to another due to osmosis, gravity, mechanical pressure, and matrix effects like capillary action is measured by water potential.

Temperature affect water potential. Water will diffuse down gradients of water potential, just as heat will flow down gradients of temperature and rocks will roll down gradients of gravitational potential.

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C: Left Meet after her events were over

The word inertia is the resistance of any physical object to any change in it's state of motion.   Things like the objects direction, speed, or it's state of rest are all included. 

Inertia can also be defined as the tendency of objects to keep moving in a straight line at it's constant velocity.