What is differential equation for the velocity of a falling object of mass m if the magnitude of the drag force is proportional to the square of the velocity and its direction is opposite to that of the velocity?

To be accurate, a scientific measuring instrument needs to be able to provide repeatable observations of a quantity.

of, pertaining to, or showing the scientific concepts or procedures. conducted scientifically or in accordance with findings of scientific investigation: by practicing or employing comprehensive or orderly procedures. advertising using science.

A scientist is a person who methodically acquires data and uses it to form hypotheses, test those assumptions and further knowledge and understanding. Additional characteristics of a scientist include: their methodology, such as their use of statistics.

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Using SOH,CAH,TOA, we can calculate the height of the building by taking the sine of the launch angle (60°) and the distance traveled (65 m). The height of the building is 56.9 m.

SOH,CAH,TOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse and Tangent = Opposite/Adjacent. This is a set of trigonometric ratios that can be used to solve for angles and lengths of sides of a right triangle. It is used when the angle and length of two sides of a right triangle are known, but the length of the third side needs to be calculated.

Calculation using SOH, CAH, TOA

The distance from the ground to the top of the building is 65 m and the angle is 60 degrees. the height (h) of the building.has to be found

Using the trigonometric ratio of Sine,  calculate the height of the building:

Sin(60°) = Opposite/Hypotenuse

h/65 = sin(60°)

h = 65sin(60°)

h = 65(0.866)

h = 56.59 m

Therefore, the height of the building the projectile was launched to from the ground is 56.59 m.

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The ball will hit the ground first if the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P as Ball A and Ball B hit the ground simultaneously.

Thus, the correct option is A.

Аccelerаtion is the rаte of chаnge in velocity, which is а vector, therefore, chаnges in this quаntity cаn influence its mаgnitude аnd/or direction. Аlthough аccelerаtion cаn be null, positive, or negаtive, it is, often, misunderstood аs а synonym for speeding up. This is true when аccelerаtion is positive for а strаight-line motion. In this type of motion, а negаtive аccelerаtion meаns thаt the object is slowing down, аnd а null аccelerаtion meаns thаt the speed does not chаnge.

Thus, when the cart moves with a constant acceleration a, and the spring is activated when the cart crosses point P, Ball A and Ball B hit the ground simultaneously.

Your question is incomplete, but most probably your full question can be seen in the Attachment.

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Answer:

Explanation:

First find the total resistance of the combination circuit:

R = V/I = 12 V / 2 A = 6 Ω

6Ω = R1 + R2 + 1/(1/R3 + 1/R4)

6Ω = 2Ω + 2Ω + 1/(1/4 + 1/R4)

2Ω = 1/(1/4Ω + 1/R4)

2Ω(1/4Ω + 1/R4) = 1

(1/4 + 1/R4) = 1/2

1/R4 = 1/4

R4 = 4Ω

Note:  R1 and R2 are in series, so you just add them together.  But R3 and R4 are in parallel, so Req = 1/R3 + 1/R4

The star with an apparent magnitude of 0.5 appears approximately 100.06 times brighter than the star with an apparent magnitude of 5.5. It is approximately 10 times closer to us.

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Answer:

1,300dollars

Explanation:

5megawatt= 5*10^6watts=5,000,000W

26cents/1000watts (10^3=kilo)

total amount=26cents/1000watts*5,000,000W

=130000cents

=1300 dollars

Might be wrong but you can try this

The distance required to be covered by the skydiver to reach the final speed is found to be 378.22m.

The deceleration produced by the parachute is -0.0302m/s². The final and the initial velocity of the skydiver are 9m/s and 83m/s respectively.

Now, we know the equation of motion,

V² - U² = 2as

Where,

V and U are the final and the initial velocity,

a is the net acceleration,

s is the distance covered by the parachute.

Now, putting all the values,

(9)²-(83)² = 2(-0.0320)s

s = 378.22 m.

So, distance that should be travelled by the skydiver is 378.22m.

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The gravitational potential energy of the car at the top of the ramp is 98,000 Joules. 

The gravitational potential energy (PE) of an object of mass m at ground level h is given by

PE = mgh

where g is the acceleration due to gravity, approximately 9.8 m/s^2 near the surface.

In this case, the car has a mass of 1000 kg and a height of 10 m above the ground. Therefore, the gravitational potential energy (PEg) is:

PEg = mgh = 1000kg * 9.8m/s^2 * 10m = 98,000J

Therefore, the gravitational potential energy of the car at the top of the ramp is 98,000 Joules. 

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1/1. For the 3500-lb car, its mass in slugs is 108.7 slug, its weight in newtons 15540 N, and its mass in kilograms is 1584 kg.  1/2. For my weight, mass in slug is 3.421 slug, weight in newton is 488.4 N, and corresponding mass in kg is 49.786 kg. 1/3. Based on the given vectors\vec{V1}+\ \vec{V2}=18i+\left(9+6\sqrt3\right)j, \vec{V1}-\ \vec{V2}=6i+\left(9-6\sqrt3\right)j, \vec{V1}\ast\ \vec{V2}=165.53\ units, \vec{V1}\ x\ \ \vec{V2}=\left(72\sqrt3-54\right)k, and \vec{V2}\ x\ \ \vec{V1}=\left(54-\ 72\sqrt3\right)k.

1/1. The weight of the car in pounds is given as 3500 lb. According to the unit conversion, as 1 lb is equal to 0.0311, the mass of the car in slugs is:

Mass = 3500 x 0.0311 = 108.7 slug

As 1 lb is equal to 4.44 N, the weight of car in newtons is:

Weight = 3500 x 4.44 = 15540 N

The equation for weight is given by:

W = mg where m is mass in kg and g is the gravity equal to 9.81 m/s^2

Hence, the mass is given by:

m=  W/g=15540/9.81=1584 kg

1/2. My weight in pounds = 110 pounds

Mass in slug = 110 x 0.0311 = 3.421 slug

Weight in newton = 110 x 4.44 = 488.4 N

Corresponding mass in kg is:

m=488.4/9.81=49.786 kg

1/3. The magnitude of vector 1 = 15 units

The magnitude of vector 2 = 12 units

The angle of inclination of vector 2 from the horizontal θ = 60∘

The vector 1 is given by:

\vec{V1}=V1\ast\left(\frac{4}{5}\right)i+V1\ast\left(\frac{3}{5}\right)j=15\ast\left(\frac{4}{5}\right)i+15\ast\left(\frac{3}{5}\right)j=12i+9j

The vector 2 is given by:

\vec{V2}=V2\ cos\theta i+V2sin\theta j=12cos60i+12sin60j=6i+6\sqrt3j

Sum of the two vectors is:

\vec{V}=\ \vec{V1}+\ \vec{V2}

\vec{V}=(12i+9j)+(6i+6\sqrt3j)

\vec{V}=\ 18i+(9+6\sqrt3)j)

Difference of the two vectors is:

\vec{V}=\ \vec{V1}-\ \vec{V2}

\vec{V}=\left(12i+9j\right)-(6i+6\sqrt3j)

\vec{V}=\ 6i+(9-6\sqrt3)j)

The dot product of the two vectors is:

\vec{V}=\ \vec{V1}\ast\ \vec{V2}

\vec{V}=\left(12i+9j\right)\ast(6i+6\sqrt3j)

\vec{V}=\ 165.530\ unit

The cross product of the two vectors is:

\vec{V}=\ \vec{V1}\ x\ \vec{V2}

\vec{V}=\left(12i+9j\right)x(6i+6\sqrt3j)

\vec{V}=\ 72\sqrt3k-54k=(72\sqrt3-54)k

The cross product of the two vectors is:

\vec{V}=\ \vec{V2}\ x\ \vec{V1}\

\vec{V}=(6i+6\sqrt3j) x \left(12i+9j\right)

\vec{V}=\ 54k-\ 72\sqrt3k=(54-\ 72\sqrt3)k

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Answer:

getting chocolate is a positive reinforcement

Explanation:

The momentum is 15817 kg-m/s rounded to the nearest whole number.

Momentum is a measure of an object's motion. It is defined as the product of an object's mass and its velocity. In mathematical terms, momentum (p) is equal to the mass (m) of an object times its velocity (v): p = m × v.

The unit of momentum is kilogram-meter per second (kg-m/s). The concept of momentum is important in physics, particularly in the study of motion, forces, and collisions. It provides a useful way of understanding and describing the motion of objects in the real world.

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Answer:

The speedometer reading of the car in km/h is 100.1 km/h. This can be calculated by using the formula K = 0.5mv2, where K is the kinetic energy, m is the mass, and v is the velocity. Rearranging this equation to solve for v yields v = √(2K/m). In this case, m = 66 kg and K = 1.1 x 104 J, so v = √(2 x 1.1 x 104 J/ 66 kg) = 100.1 km/h.

The rock thrown straight up will have less speed at impact compared to the rock thrown straight down.

The rock that was thrown straight up will experience slower speed at impact due to the effect of gravity. As the rock rises, gravity will slow its velocity and increase its potential energy. At the highest point, its velocity will be zero and its potential energy will be at a maximum.

As the rock falls back down, it will convert potential energy back into kinetic energy, reaching its maximum speed just before impact. The rock thrown straight down, on the other hand, will not experience any change in velocity as it falls due to gravity, leading to a higher speed at impact.

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The fraction of energy lost by the colliding body is 8/9.

In an elastic collision, the total kinetic energy of the system before the collision is equal to the total kinetic energy of the system after the collision.

Before the collision, the total kinetic energy of the system is given by:

[tex]K1 = 0.5 * m1 * u^2[/tex]

After the collision, the total kinetic energy of the system is given by:

[tex]K2 = 0.5 * m_{1} * v_{1} ^2 + 0.5 * m_{2} * v_{2}^2[/tex]

where m1 is the mass of body A, u is its initial velocity, v1 is its final velocity, m2 is the mass of body B, and v2 is its final velocity.

Conservation of momentum also applies in this case. The momentum of the system before the collision is equal to the momentum of the system after the collision.

Before the collision, the momentum of the system is given by:

[tex]p_{1} = m_{1} * u[/tex]

After the collision, the momentum of the system is given by:

[tex]p_{2} = m_{1} * v_{1} + m_{2} * v_{2}[/tex]

From the conservation of momentum, we have:

[tex]m_{1} * u = m_{1} * v_{} + m_{2} * v_{2}[/tex]

Solving for v1 and v2, we find:

[tex]v_{1} = u * (m_{1} - m_{2}) / (m_{1} + m_{2})[/tex]

[tex]v_{2} = 2 * u * m_{1} / (m_{1} + m_{2})[/tex]

Substituting these values into the equation for K2, we find:

[tex]K_{2} = 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]

The fraction of energy lost by body A is given by:

[tex](K_{1} - K_{2}) / K_{1} = 1 - K_{2} / K_{1}[/tex]

= [tex]1 - 0.5 * m_{1} * u^2 * (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2 / (0.5 * m_{1} * u^2)[/tex]

= [tex]1 - (m_{1} - m_{2})^2 / (m_{1} + m_{2})^2[/tex]

= 1 - (4 - 2)^2 / (4 + 2)^2

= 1 - (2)^2 / (6)^2

= 1 - 4/36 = 1 - 1/9 = 8/9

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As the temperature of the flask increases, the molecules in the air become more energetic, resulting in an increase in air pressure.

Given the total pressure measured for the each trail = vapor pressure of liquid +  pressure due to any air trapped in the flask.

a) The pressure of the gas rises because the molecules collide with the container walls more frequently as a result of the faster collisions between the molecules and the walls. This is because the molecules are moving faster and collide more often with the walls of the flask, creating a greater force.

b) To calculate the corrected air pressure, the ideal gas law can be used (P1/T1 = P2/T2). The atmospheric pressure (P1) and temperature (T1) must be known for the trial and the temperature (T2) of the flask must be known. The corrected air pressure (P2) can then be calculated.

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The 2.5 kg block pulls on the 9 kg block with an 87.2 N force.

Newton's Third Law, often known as the law of action and reaction, can be used to determine the force that the 2.5 kg block exerts on the 9 kg block. The force applied to the 9 kg block is equivalent to, but applied in the opposite direction from, the force applied to the 2.5 kg block. Since they are in touch, the force of friction operating on the 9 kg block is equal to the force of friction acting on the 2.5 kg block.

Calculating the friction force is as simple as multiplying the normal force, or weight of the object, by the coefficient of friction:

Step 1: Determine the normal force or weight of the object. The weight of a 9 kg object can be calculated as 9 kg x 9.8 N/kg = 87.2 N.

Step 2: Determine the coefficient of friction. In this case, the coefficient of friction is 0.1.

Step 3: Calculate the friction force by multiplying the normal force by the coefficient of friction.

Friction force = Normal force x Coefficient of friction

= 87.2 N x 0.1 = 8.72 N.

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Heat and work are path functions because their values depend on the path taken from the initial to the final state of a system.

Heat is a form of energy that is transferred from one object to another due to a difference in temperature. Heat is a form of kinetic energy, the energy of motion, and can be transferred from one object to another by conduction, convection, and radiation.

Both heat and work can cross the boundary of a system, as energy transfer in the form of heat or work can occur when a system interacts with its surroundings.
Heat and work are associated with a process, which is a change in the state of a system from one thermodynamic state to another.
Heat and work are also associated with a thermodynamic state, as the amount of heat and work exchanged between a system and its surroundings is determined by the thermodynamic state of the system.
Finally, systems possess energy in the form of heat and work, which can be exchanged between a system and its environment.

Therefore, all the given option is correct
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the direction for each of three successive vehicles. A = {RRR,LLL,SSS} ,  B = {RLS, RSL, LSR, LRS, SRL, SLR} C = {RRS, RRL, RSR, RLR, LRR, SRR}

Direction is defined as the path that something takes, the path that must be taken to reach a specific place, the way in which something is starting to develop or the way you are facing. An example of direction is when you go right instead of left.

the course or path on which something is moving or pointing. The army attacked from three different directions. Down the road, he could see a bus coming from the opposite direction. The wind changed direction and started blowing in  faces.

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The correct statement is (c): At the highest point in its motion, the ball's velocity is zero.

This is due to the fact that when anything is thrown straight up, it has a starting velocity and then accelerates as it descends towards the Earth. Its velocity is equal to zero as it reaches its highest point (due to the gravitational pull of the Earth). The ball's acceleration varies continuously as it travels because it accelerates towards the Earth when it is travelling upward and decelerates when it is travelling downward.

The ball is briefly at rest, and the only force acting on it is the gravitational pull of the Earth, therefore at its fastest point in motion, the acceleration is equal to zero.

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The density measures the compactness of a substance. Here the density of an object of mass 60 g and volume 150 cm³ is 0.4 g/cm³.

The mass of an object contained per unit volume is defined as the density. The SI unit of density is kg / m³. The equation used to calculate density is:

Density = Mass / Volume

= 60 / 150 = 0.4 g/cm³

The objects which have same volume, but different masses have different densities. If greater the mass, more dense will be the object.

Thus the density of the object is 0.4 g/cm³.

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After comparing the force of gravity on the Moon due to the Earth, and the force of gravity on the Earth due to the Moon, we find that The forces are equal and opposite. Thus, option B is correct.

The force that unites all matter is called gravity (which is anything you can physically touch). The gravitational pull of objects with a lot of matter, such as planets, moons, and stars, increases with their mass.

The quantity of matter in something is determined by its mass. Everything has a gravitational pull, and this pull increases with mass. The Earth pulls on us as we walk on its surface, and we yank back in response. The Earth's pull can cause us to fall to the ground, whereas our pull is insufficient to move the Earth because it is so much heavier than we are.

In this system both the objects have mass so the gravitational force between them is,  

[tex]$\mathrm{F = \frac{GM_1M_2}{R_2} }[/tex]

For the earth moon system,

[tex]$\mathrm{F_{e/m} = \frac{GM_eM_m}{R_2} }[/tex] and [tex]$\mathrm{-F_{m/e} = \frac{GM_eM_m}{R_2} }[/tex]here negative sign stands for opposite direction.

According to Newton's third law of motion, gravitational forces from the earth to the moon are equal but opposite in direction. Because the gravitational force formula is based on the masses of both objects, the formula applies to both objects.

Therefore, B. The forces are equal and opposite is correct.

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After n half-lives, its radioactivity will be 100× [tex]2^{-n}[/tex] Bq.

A characteristic of some forms of matter known as radioactivity is the spontaneous emission of energy and subatomic particles. In essence, it is a characteristic of particular atomic nuclei.

The radioactivity of the material is 100 Bq, that means, the radioactivity of the material is 1000 disintegration per second.

the relation between radioactivity and half-life is : A = A₀ 2^-n

Hence, after n half-lives, its radioactivity will be = 100 × 2^-n Bq.

Therefore, after n half-lives, its radioactivity will be 100× [tex]2^{-n}[/tex] Bq.

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Answer:

You can show respect for others' intellectual property by:

Answer:

see below

Explanation:

the given circuit comprises of a 10V battery and 2Ω and 6Ω resistance. The resistances are connected in parallel, so we can find the net resistance as ,

[tex]\implies \dfrac{1}{R_n}=\dfrac{1}{R_1}+\dfrac{1}{R_2} \\[/tex]

[tex]\implies R_n =\dfrac{R_1R_2}{R_1+R_2} \\[/tex]

[tex]\implies R_n =\dfrac{2\times 6 }{2+6}\Omega \\[/tex]

[tex]\implies R_n =\dfrac{12}{8}\Omega\\[/tex]

[tex]\implies R_n = 1.5\Omega \\[/tex]

Now from Ohm's law, we have,

[tex]\implies V = iR \\[/tex]

where ,

[tex]\implies 10V = i \times 1.25\Omega \\[/tex]

[tex]\implies i =\dfrac{10}{1.25} A \\[/tex]

[tex]\implies \underline{\underline{ i = 8A }}\\[/tex]

and we are done!

The distance that is covered is 8.5 m.

We have to note that the movement of the dart would be the movement of a parabola. We would need to know that in this case, the first thing that we should find is the time that has been taken;

t = u sin 45/0.5 * 9.8

t = 9.12 sin 45/0.5 * 9.8

t = 1.32 s

Then we have that;

R = Vxt

Thus the distance that is covered is;

R = 9.12 cos45 * 1.32

R = 8.5 m

We can see that the projectile movement of the dart would cover a horizontal distance of about 8.5 m

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Answer:

Explanation:

The velocity of each ball after the collision can be determined using the law of conservation of momentum. The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces are acting on the system. In this case, the two balls form an isolated system before and after the collision, so their total momentum must be conserved.

Let's call the velocity of the heavier ball after the collision "v". The total momentum before the collision is given by:

p_i = (0.600 kg)(4.00 m/s) + (1.00 kg)(-5.00 m/s) = -2.00 kg m/s

The total momentum after the collision is given by:

p_f = (0.600 kg)(v) + (1.00 kg)(-7.25 m/s) = 0.600 kg v - 7.25 kg m/s

Since the total momentum is conserved, we can set the initial momentum equal to the final momentum and solve for v:

p_i = p_f

-2.00 kg m/s = 0.600 kg v - 7.25 kg m/s

Adding 7.25 kg m/s to both sides and dividing both sides by 0.600 kg, we get:

v = (2.00 kg m/s + 7.25 kg m/s) / 0.600 kg = 9.25 m/s

So, the velocity of the heavier ball after the collision is 9.25 m/s.

Answer:

The velocity of the heavier ball after the collision is 3.05 m/s

Explanation:

This is an example of partially elastic collision. In a partially elastic collision, momentum is conserved and the objects move at different speeds. A portion of the initial kinetic energy is still retained by the colliding objects after the impact.

The conservation of momentum states that the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

The formula for momentum is

[tex]p=mv[/tex]

We can conclude that

[tex]m_1v_{1i} +m_2v_{2i}=m_1v_{1f} +m_2v_{2f}[/tex]

Let object 1 be the 0.600 kg ball.

Let object 2 be the 1.00 kg ball.

We are given

[tex]m_1=0.600\\v_{1i} =4.00\\m_2=1.00\\v_{2i} =5.00\\v_{1f} =7.25[/tex]

Inserting our given values into the equation gives us

[tex](0.600*4.00)+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]

Lets solve for [tex]v_{2f}[/tex].

Evaluate each set of parenthesis.

[tex]2.4+(1.00*5.00)=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]

[tex]2.4+5=(0.600*7.25)+\left(1.00*v_{2f}\right)[/tex]

[tex]2.4+5=4.35+\left(1.00*v_{2f}\right)[/tex]

Anything multiplied by 1 stays the same.

[tex]2.4+5=4.35+v_{2f}[/tex]

Add 2.4 and 5.

[tex]7.4=4.35+v_{2f}[/tex]

Subtract 4.35 from both sides of the equation.

[tex]3.05=v_{2f}[/tex]

The correct answer is (A) b < d < c < a.

we need to consider the placement of the resistors.

In circuits a, b and c, resistors are connected in series. The corresponding resistance of resistors combined in series is the sum of the particular resistances. So the equivalent resistance for these circuits is:

a) 3R + R + 3R = 7R

b) R + R + 3R + 3R = 8R

c) 3R + R + R + 3R = 8R

In circuit d, resistors are connected in parallel. The equivalent resistance of resistors connected in parallel is given by the formula

1/request = 1/R + 1/R + 1/R = 3/R

Therefore Req = R/3. Comparing the values ​​of the equivalent resistors reveals the following:

b < d < c < a

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Answer:

2.8 A

Explanation:

since the resistances are in series, the net resistance will be,

R = R1 + R2 + R3 + .....

R = ( 5+10+12+16)Ω

R = 43Ω

From Ohm's law,

V = iR

120 = i * 43

i = 120/43 A

i = 2.8A