a projectile is launched at an angle of 600 with respect to the horizontal and with initial speed of 30 m/s. what is the horizontal range of the projectile?

A body starts from rest and travels for t seconds with uniform acceleration of 2m/s². If the displacement made by it is 16m the time of travel t will be 4 seconds.

If an object is traveling in a straight line path and its velocity increases or decreases by the equal amounts in equal intervals of time, then the acceleration of the object will be said to be uniform.

The time can be calculated through 2nd equation of motion.

s = ut + ½ at²

Given,

s = 16m      

a = 2m/s²

u = 0 (since the body starts from rest)

So,

16 = (0)t + 1/2(2) (t)²

After solving it,

16 = t²

t = 4

Therefore, the time of travel is 4 seconds.

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The several forms of businesses that exists in our current world include;

A business refers to a commercial activity that an individual or organization engage in which may involve other activities which support the main activity of the business.

When the word business is heard, what usually comes to mind is the activity that occurs in stores which involves buying and selling of produce and goods.

However, several forms of businesses exists such as;

In conclusion, the sole aim of a business is to make profit whether it involves commercial activities or not.

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The x and y components of the net force, F is 4.33N + 17.5N. The magnitude is 18.02 N and the direction is 76.10 N.

The initial velocity is Vi = 3 m/s

(a) F₁x = Fcosθ

Or,  F₁x = 5Ncos30

Or,  F₁x = 4.33 N

F₁y = Fsinθ

F₁y = 5Nsin30

Or, F₁y = 2.5 N

F₂x = 0

F₂y = 15Nsin30

F₂y = 2.5 N

Therefore, the net force is, F = 4.33N + 17.5N

(b) The magnitude of the net force is

F =√Fx² + Fy²

F = √(4.33)² + (1.75)²

F = 18.02 N

So, the magnitude is 18.02 N.

The direction is

θ = Tan⁻¹[Fy/Fx]

Or, θ = Tan⁻¹ [17.5/4.33]

θ = 76.10 N

The direction of the net force is 76.10 N.

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Answer:

The untrue option is C: "More arrowheads on lines mean a brighter light"

Explanation:

Ray diagrams are used to show how the light behaves with things like mirrors or lenses. Where we only study how the direction of the light changes when it interacts with these objects.

The "light" is represented with arrows, where again, the only thing we care is the direction of the light, so the first statement is true, the arrowheads show the direction of the light, and only that.

The intensity of the light, in this context, has no effect on how light behaves, so there is not a necessity of representing the intensity of the light, thus, more arrowheads on lines do not mean a brighter light. It may only be used to represent changes in direction of the light.

Finally, we know that light travels in straight pats (the pats can be curved in some cases, like with large gravitational fields, but this is not the case of a ray diagram) so the lines that represent the light should always be straight, thus option B is also true.

The untrue option is C: "More arrowheads on lines mean a brighter light"

Answer:

"For towing, a tow chain should be of a length that keeps both vehicles within the maximum 4.5 meter distance, also  tow chains an be any length 20 foot chains are often chosen"  

Explanation:

-  https://letstowthat.com

Also Quick note the feet of tow rope or chain varies on the situation but most longest or 20 feet.  

The average speed of a car can be calculated by dividing the distance traveled by the time taken. In this case, the car travels a distance of 53.1 km in a time of 28.3 minutes.

To find the average speed in km/h, we need to convert the time from minutes to hours since the distance is given in kilometers.

There are 60 minutes in an hour, so to convert 28.3 minutes to hours, we divide it by 60:

28.3 minutes ÷ 60 = 0.4717 hours (rounded to four decimal places)

Now, we can calculate the average speed by dividing the distance by the time:

Average speed = distance ÷ time

Average speed = 53.1 km ÷ 0.4717 hours = 112.618 km/h (rounded to three decimal places)

Therefore, the average speed of the car is approximately 112.618 km/h.

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Answer:

Gamma rays are mostly used in the radiotherapy/ radiooncology to treat cancer. They can also be used to spot tumours. Gamma rays can kill living cells and damage malignant tumor

Answer: B. Ax = 6, Ay=8

Explanation:

Answer:

B.d

mark me as brainlist

Answer:

D. b

Explanation:

the endpoint of vector b is at 3, which means the length is 3

Answer:

See the explanation below.

Explanation:

Newton's third law states that any force applied to a body generates a reaction equal and in opposite direction to the original Force.

In order to better understand how a person's movement is generated when walking, we will analyze the attached image below, where we see the forces acting.

The red vector goes in the direction of the person's movement, this force vector pushes the person to move forward.

Answer:

5 years

Explanation:

\(\frac{1}{8}(40)\\\\= 5\)

The relative humidity is 50%, indicating the air is holding half of the moisture it can hold at the current temperature, aiding in weather predictions.

Given that an air parcel is sinking 1 km, the temperature in the parcel increases by 10 degrees C, but the vapor pressure remains constant. The vapor pressure in the parcel is 10 hPa, and the saturation vapor pressure is 20 hPa within the parcel. To calculate the relative humidity, we use the formula: Relative Humidity = Vapor pressure / Saturation vapor pressure * 100.

Plugging in the given values, we have: Relative humidity = 10 / 20 * 100. Simplifying the equation, we find that the relative humidity is 50%.

A relative humidity of 50% indicates that the air is holding half the amount of moisture it is capable of holding at the current temperature. This measure is crucial in meteorology as it helps forecasters predict cloud formation, precipitation, and other weather phenomena.

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The main reason hydrogen-driven automobiles have not replaced gasoline ones is the lack of infrastructure and production challenges.

Here's a step-by-step explanation:
1. Infrastructure: Hydrogen fueling stations are not as widespread as gasoline stations. This lack of infrastructure makes it inconvenient for consumers to refuel their hydrogen-powered vehicles easily.
2. Production challenges: Hydrogen fuel is primarily produced through a process called steam methane reforming, which requires natural gas. This process contributes to carbon emissions, limiting the environmental benefits of hydrogen-powered vehicles. Additionally, producing and storing hydrogen can be costly and challenging.
3. Cost: Hydrogen fuel cell vehicles are generally more expensive than gasoline-powered vehicles. The high cost of production, including the manufacturing of fuel cells and hydrogen storage systems, makes these vehicles less affordable for the average consumer.
4. Limited range: Hydrogen-powered vehicles have a limited range compared to gasoline vehicles. This is due to the lower energy density of hydrogen fuel compared to gasoline, meaning that hydrogen-powered vehicles require larger storage tanks or more frequent refueling.
In conclusion, the main reasons hydrogen-driven automobiles have not replaced gasoline ones are the lack of infrastructure, production challenges, higher costs, and limited range. Overcoming these challenges will be crucial for the widespread adoption of hydrogen-powered vehicles in the future.

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Answer:

Once you have drawn the free-body diagram, you can use vector addition to find the net force acting on the object. We will consider three cases as we explore this idea:

Case 1: All forces lie on the same line.

If all of the forces lie on the same line (pointing left and right only, or up and down only, for example), determining the net force is as straightforward as adding the magnitudes of the forces in the positive direction, and subtracting off the magnitudes of the forces in the negative direction. (If two forces are equal and opposite, as is the case with the book resting on the table, the net force = 0)

Example: Consider a 1-kg ball falling due to gravity, experiencing an air resistance force of 5 N. There is a downward force on it due to gravity of 1 kg × 9.8 m/s2 = 9.8 N, and an upward force of 5 N. If we use the convention that up is positive, then the net force is 5 N - 9.8 N = -4.8 N, indicating a net force of 4.8 N in the downward direction.

Case 2: All forces lie on perpendicular axes and add to 0 along one axis.

In this case, due to forces adding to 0 in one direction, we only need to focus on the perpendicular direction when determining the net force. (Though knowledge that the forces in the first direction add to 0 can sometimes give us information about the forces in the perpendicular direction, such as when determining frictional forces in terms of the normal force magnitude.)

Example: A 0.25-kg toy car is pushed across the floor with a 3-N force acting to the right. A 2-N force of friction acts to oppose this motion. Note that gravity also acts downward on this car with a force of 0.25 kg × 9.8 m/s2= 2.45 N, and a normal force acts upward, also with 2.45 N. (How do we know this? Because there is no change in motion in the vertical direction as the car is pushed across the floor, hence the net force in the vertical direction must be 0.) This makes everything simplify to the one-dimensional case because the only forces that don’t cancel out are all along one direction. The net force on the car is then 3 N - 2 N = 1 N to the right.

Case 3: All forces are not confined to a line and do not lie on perpendicular axes.

If we know what direction the acceleration will be in, we will choose a coordinate system where that direction lies on the positive x-axis or the positive y-axis. From there, we break each force vector into x- and y-components. Since motion in one direction is constant, the sum of the forces in that direction must be 0. The forces in the other direction are then the only contributors to the net force and this case has reduced to Case 2.

If we do not know what direction the acceleration will be in, we can choose any Cartesian coordinate system, though it is usually most convenient to choose one in which one or more of the forces lie on an axis. Break each force vector into x- and y-components. Determine the net force in the x direction and the net force in the y direction separately. The result gives the x- and y-coordinates of the net force.

Example: A 0.25-kg car rolls without friction down a 30-degree incline due to gravity.

We will use a coordinate system aligned with the ramp as shown. The free-body diagram consists of gravity acting straight down and the normal force acting perpendicular to the surface.

We must break the gravitational force in to x- and y-components, which gives:

F_{gx} = F_g\sin(\theta)\\ F_{gy} = F_g\cos(\theta)F

gx

​

=F

g

​

sin(θ)

F

gy

​

=F

g

​

cos(θ)

Since motion in the y direction is constant, we know that the net force in the y direction must be 0:

F_N - F_{gy} = 0F

N

​

−F

gy

​

=0

(Note: This equation allows us to determine the magnitude of the normal force.)

In the x direction, the only force is Fgx, hence:

F_{net} = F_{gx} = F_g\sin(\theta) = mg\sin(\theta) = 0.25\times9.8\times\sin(30) = 1.23 \text{ N}F

net

​

=F

gx

​

=F

g

​

sin(θ)=mgsin(θ)=0.25×9.8×sin(30)=1.23 N

The motion of the mass is described by a simple harmonic motion equation, with the radian frequency ω = √5 rad/s. The cyclic natural frequency (f) is the reciprocal of the period (T), and the period of oscillation is approximately 2.82 seconds.

a. The motion of the mass can be described by a simple harmonic motion equation. The restoring force exerted by the spring is proportional to the displacement of the mass from its equilibrium position. The equation of motion can be written as:

m * a = -k * x

Where m is the mass (2 kg), a is the acceleration, k is the spring constant (10 N/m), and x is the displacement from the equilibrium position.

Using Newton's second law, we can rewrite the equation as:

m * d^2x/dt^2 = -k * x

This is a second-order linear differential equation that describes the motion of the mass.

b. The radian frequency (ω) is given by the formula:

ω = √(k / m)

Substituting the given values, we have:

ω = √(10 N/m / 2 kg) = √5 rad/s

c. The cyclic natural frequency (f) is the reciprocal of the period (T) and can be calculated as:

f = 1 / T

d. The period of oscillation (T) can be found using the formula:

T = 2π / ω

Substituting the value of ω, we get:

T = 2π / √5 ≈ 2.82 s

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Answer: 1/10th of its weight on Earth.

Explanation: Let's assume that the weight of the object on Earth is W, and the gravitational acceleration on Earth is g. We know that weight is given by the formula:

W = m * g where m is the mass

If the gravitational attraction on another planet is 1/10th of Earth's pull, then the gravitational acceleration on that planet will be:

g' = g/10

Using the same formula for weight, the weight of the object on the new planet will be:

W' = m * g'

Substituting the value of g' in the equation above, we get:

W' = m * (g/10)

W' = (m/10) * g

Therefore, the weight of the object on the new planet will be 1/10th of its weight on Earth.

W' = (100/10) N = 10 N

So, the weight of the same object on a planet where the gravitational attraction has been reduced to 1/10th of Earth's pull would be 1/10th of its weight on Earth.

The value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

When an object collides with another object, they exchange energy. For example, a baseball and bat collision or a car collision. When two objects collide, the force of the collision has to be equal on both sides of the collision according to Newton's Third Law. So, to find the value of force, we will apply the equation:

F = ΔP / ΔT

where F is the force, ΔP is the change in momentum, and ΔT is the time of collision. The equation represents the impulse momentum theorem.

Now, let's apply the given values to the above equation.

Final momentum (p2) = mass × final velocity (v2)

p2 = 0.15 kg × (-50 m/s)

p2 = -7.5 kg.m/s

Initial momentum (p1) = mass × initial velocity (v1)

p1 = 0.15 kg × (40 m/s)

p1 = 6 kg.m/s

Change in momentum (ΔP) = p2 - p1

ΔP = -7.5 kg.m/s - 6 kg.m/s

ΔP = -13.5 kg.m/s

Time of collision (ΔT) = 8.0 × 10³ s

Now, putting the values of ΔP and ΔT in the equation of impulse momentum theorem, we get:

F = ΔP / ΔT

F = -13.5 kg.m/s ÷ 8.0 × 10³ s

F = -1.7 × 10⁻³ N

Thus, the value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

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To determine the mass of granite, we must first understand the definition of density. Density is defined as the amount of matter present in a substance per unit volume.

We use the formula: density = mass/volume to calculate the mass of a substance given its density and volume. To calculate the mass of 54.3 m³ of granite, we use the following steps:

Given Density of granite = 2700 kg/m³Given volume of granite = 54.3 m³Let us substitute the values in the formula of density:density = mass/volume Solving for mass, we get:mass = density × volume Substitute the given values of density and volume into the formula:mass = 2700 kg/m³ × 54.3 m³

The m³ unit in the volume cancels out, leaving us with kg as the unit for mass.

We then solve the equation to get the mass:mass = 146,610 kg

Therefore, the mass of 54.3 m³ of granite is 146,610 kg.

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a) The correct average velocity of the man is approximately 0.026928 km/h.

b) The correct average speed of the man is approximately 0.03726 km/h.

a) Average Velocity:

To calculate the average velocity, we need to determine the total displacement and divide it by the total time taken.

The north displacement is 28.125 m and the east displacement is 18.45 m. Since we are given that each block represents 1 km, we need to convert these distances to kilometers.

North displacement: 28.125 m ÷ 1000 = 0.028125 km

East displacement: 18.45 m ÷ 1000 = 0.01845 km

The total displacement can be calculated using the Pythagorean theorem:

Total displacement = √((0.028125 km)² + (0.01845 km)²) = √(0.000790039 km² + 0.0003409025 km²) ≈ √0.001130941 km² ≈ 0.03366 km

Since the total time taken is given as 1.25 hours, the average velocity is calculated by dividing the total displacement by the total time:

Average velocity = Total displacement ÷ Total time = 0.03366 km ÷ 1.25 hours ≈ 0.026928 km/h

Therefore, the correct average velocity of the man is approximately 0.026928 km/h.

b) Average Speed:

To calculate the average speed, we need to determine the total distance traveled and divide it by the total time taken.

The total distance traveled is obtained by summing up the north and east distances:

Total distance = 0.028125 km + 0.01845 km = 0.046575 km

Average speed = Total distance ÷ Total time = 0.046575 km ÷ 1.25 hours ≈ 0.03726 km/h

Therefore, the correct average speed of the man is approximately 0.03726 km/h.

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The potential energy  and kinetic energy of the bowling ball are 2,205 J and 37.5 J respectively.

The bowling ball at the given position and speed possess gravitational potential energy and kinetic energy.

The potential energy  and kinetic energy of the bowling ball is calculated as follows;

P.E = mgh

where;

P.E =  (3 x 9.8 x 75 )

P.E = 2,205 J

The kinetic energy of the bowling ball is calculated as;

K.E = ¹/₂ mv²

where;

K.E = ¹/₂ ( 3 ) x (5²)

K.E = 37.5 J

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Explanation:

A particle accelerator is a machine that uses electric fields to accelerate charged particles to very high speeds and energies. These particles are then collided with a target or another beam of particles. The resulting collision products are then studied by detectors to learn more about the fundamental nature of matter and the universe.

One example of a particle accelerator is the Large Hadron Collider (LHC) at CERN. The LHC is used to collide beams of protons or lead ions at very high energies. By studying the collisions, scientists have been able to discover new subatomic particles, such as the Higgs boson, and test fundamental theories of particle physics, such as the Standard Model. The discoveries made at the LHC have helped to deepen our understanding of the building blocks of matter and the origins of the universe.

The cyclotron accelerates the charged particles in the magnetic field by applying an alternating electric field.

A particle accelerator is a machine that accelerates charged particles higher speed and energy, by using electromagnetic field.

Here,

The particle accelerator uses electromagnetic field for accelerating the charged particles and finally for colliding them on a target.

Cyclotron is  an application of particle accelerator.

Cyclotron is a device used to accelerate heavy, charged particles or ions like proton, deuteron, He nucleus etc.

Cyclotron consists of two semicircular D shaped discs called dees, at the centre of which an ion source is placed. An electromagnet is placed at the both ends of the plates.

The principle of cyclotron is that, a charged particle entering perpendicular to a magnetic field can create a circular path.

Ions or charged particles are released into the dees. These ions moves in a circular path due to the perpendicular magnetic field.

An alternating voltage is applied between the dees, such that it accelerates the charged particles.

Hence,

The cyclotron accelerates the charged particles in the magnetic field by applying an alternating electric field.

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(a) A = B × r is a vector potential for B, where r = {x, y, 0}.

(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.

(a) To verify that A = B × r is a vector potential for B, we need to show that ∇ × A = B.

Using the cross product property, we have ∇ × A = ∇ × (B × r). Applying the vector identity (A × B) × C = B(A · C) - C(A · B), we get ∇ × (B × r) = B(∇ · r) - r(∇ · B).

Since ∇ · r = 0 (as r = {x, y, 0}), and ∇ · B = 0 (as B has a constant magnitude in the z-direction), we find that ∇ × A = B, verifying A = B × r as the vector potential for B.

(b) The flux through a surface S can be calculated as Φ = ∫B·dA, where B is the magnetic field and dA is an infinitesimal area vector perpendicular to the surface.

Given that B has a constant strength b teslas in the z-direction, the flux through surface S will be Φ = ∫B·dA = ∫(0, 0, b) · (dxdy) = b∫dxdy = bA, where A is the area of the surface S.

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Cystic fibrosis is a recessive genetic disorder caused by a mutation in the CFTR gene. It affects the lungs, pancreas, and other organs, causing difficulties in breathing and digestive problems.

Hemophilia is an X-linked recessive genetic disorder that affects blood clotting due to mutations in clotting factor genes. Hemophilia A is caused by a mutation in the F8 gene while hemophilia B is caused by a mutation in the F9 gene.

Duchenne muscular dystrophy is an X-linked recessive genetic disorder caused by mutations in the DMD gene, which codes for a protein called dystrophin. It affects muscle function and leads to muscle weakness and wasting.

Huntington's disease is an autosomal dominant genetic disorder caused by a mutation in the HTT gene. It affects brain function, leading to psychiatric symptoms and movement problems.

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Cystic fibrosis -  autosomal recessive pattern, Hemophilia -  X-linked recessive pattern, Duchenne muscular dystrophy -  X-linked recessive pattern and Huntington's disease - autosomal dominant pattern.

Gene alterations that are essentially present in every cell in the body cause many hereditary diseases. These illnesses thus frequently impact many bodily systems, and the majority cannot be treated. To treat or manage some of the accompanying symptoms, there might be methods available.

Genetic disorders connected to mutations in genes on the X chromosome are referred to as having X-linked recessive inheritance. Because he contains just one X chromosome, a male who carries this mutation will be affected. A female who carries a gene mutation in one X chromosome but has a normal gene on the other X chromosome usually has no symptoms.

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The threshold energy needed to force an electron out of silver, expressed in j, is: 7.59 × 10^-19

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The way that Q and W are related during the isobaric part of the overall path is that W provides energy output, while Q provides energy input; Q is larger. Option A.

A thermodynamic process called an isobaric process keeps the pressure constant. This is typically accomplished by allowing the volume to alter in size in order to balance off any pressure changes brought on by heat transfer.

Vb > Vd

W tends towards the positive. This is the energy output of the system. The pressure is constant so Q is energy input. Hence the first option is the correct one

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Question

how are q and w related during the isobaric part of the overall path from state d to state b?

1. W provides energy output, while Q provides energy input; Q is larger

2. Both W and Q provide energy input

Answer:

The force due to gravity is called weight. It can be resolved into two axes: along the ramp and normal to the ramp. The ramp angle is 30 degrees so we have

m.g.sin(30) = 25 . 10. 0.5 (parallel) = 125N

and

m.g.cos(30) = 25 . 10 . 0.8660 (normal) = 216.5 N

Work is given by force times distance IN THE DIRECTION OF THE FORCE

so the work due to the parallel gravity force is opposite the direction of the motion; and we signal that with a minus sign: 125 x -3 = -375 joules.

But hang on a durned minute!

Explanation:

The work done by the weight (gravitational force) of the box will be - 375 N

The work done by a force can be defined as the product of the displacement of an object and the component of the applied force which is in the direction of the object's displacement.

mg (gravity ) will have two components

1) parallel component : mg sin(theta)

2) perpendicular component : mg cos (theta)

m*g*sin(30) = 25 * 10 * 0.5 = 125N

m*g*cos (30) = 25 * 10*0.8660 = 216.5 N

work done = F s cos (x)

work done = force * displacement * cos(x)

                 = 125 * 3 * cos(180)

                 = 125 * 3 * (-1)

                 = - 375 N

The work done by the weight (gravitational force) of the box will be - 375 N

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Answer:

force (tension) of 29.4 N (upward)  in 100 cm

force (tension) of 58.4 N (upward)  in 200 cm

Explanation:

Given:

Length of tube = 5 m (500 cm)

Mass of tube = 9

Suspended vertically from 150 cm and 50 cm.

Computation:

Force = Mass × gravity acceleration.

Force = 9.8 x 9

Force = 88.2 N

So,

Upward forces = Downward forces

D1 = 150 - 50 = 100 cm

D2 = 150 + 50 = 200 cm

And F1 = F2

F1 x D1 = F2 x D2

F1 x 100 = F2 x 200

F = 2F

Total force = Upward forces + Downward forces

3F = 88.2

F = 29.4 and 2F = 58.8 N

force (tension) of 29.4 N (upward)  in 100 cm

force (tension) of 58.4 N (upward)  in 200 cm

"Constant velocity" means that there is no acceleration. Acceleration = 0 .

So its graph is zero at every time. The line on the graph lies on the X-axis.