A stone is thrown horizontally from a vertical cliff at a speed of 20 meters per second. The cliff is 30 meters above sea level and the
stone hits the sea after 2.5 seconds.
How far from the base of the cliff is the stone when it hits the sea? (g = 10 m/s)
1.5 POINTS

The typical canoeist can paddle at about 2.6 knots, or 3 mph (ca. 5 km/h), when paddling without stopping and in calm, quiet water. Obviously, the length of time depends on the weather, the person's health, and the speed of the canoe.

The typical canoeist can paddle at about 2.6 knots, or 3 mph (ca. 5 km/h), when paddling without stopping and in calm, quiet water. Obviously, the length of time depends on the weather, the person's health, and the speed of the canoe.

Therefore, When the medium is deepest, water waves propagate more quickly. Water waves will therefore slow down as they go from deep to shallow water.

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The statement "short-wave (visible and ultraviolet) radiation that reflects off the Earth's surface is absorbed by the lower atmosphere and heats it up, a process otherwise known as the greenhouse effect" is true.

Solаr energy аbsorbed аt Eаrth’s surfаce is rаdiаted bаck into the аtmosphere аs heаt. Аs the heаt mаkes its wаy through the аtmosphere аnd bаck out to spаce, greenhouse gаses аbsorb much of it. Greenhouse gаses аre more complex thаn other gаs molecules in the аtmosphere, with а structure thаt cаn аbsorb heаt. They rаdiаte the heаt bаck to the Eаrth's surfаce, to аnother greenhouse gаs molecule, or out to spаce.

Eаrth is constаntly bombаrded with enormous аmounts of rаdiаtion, primаrily from the sun. This solаr rаdiаtion strikes the Eаrth's аtmosphere in the form of visible light, plus ultrаviolet (UV), infrаred (IR) аnd other types of rаdiаtion thаt аre invisible to the humаn eye. UV rаdiаtion hаs а shorter wаvelength аnd а higher energy level thаn visible light, while IR rаdiаtion hаs а longer wаvelength аnd а weаker energy level.

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A proton (charge 1.602 * 10-19) moves a distance of d= 0.59 m from point A to point B in a straight line inside a linear accelerator. The electric field of the accelerator is uniform and has a magnitude of 15 MN/C.

i.) The expression for the force on proton is,

F=qE

(1.6⋅10−19 )(1.5⋅10 7)

=2.4⋅10 −12 N

Thus, the force on the proton is 2.4⋅10 −12 N.

ii) The expression for the work done by the field is,

W=qEd

(1.6⋅10 −19)(1.5⋅10 7 )(0.5)

=1.2⋅10 −12J

iii) The expression for the potential difference is,

U=Ed

=(1.5⋅10 7) (0.5)

=0.75⋅10 7 V

Electric potential of a system of point charges?

A point charge's electric potential is V=kQ/r. Electric field is a vector while electric potential is a scalar.

What is the electric potential at a point distance?

Electric potential at point P, located at a distance of r=R2 from the center, where R is the radius of an evenly charged shell with a density of surface charges.

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Both boxes have the same amount of kinetic energy as each other (option- b) is correct.

If no energy is lost through friction, the system's mechanical energy stays constant. When the speed picks up, the energy would change into kinetic energy. Providing there is no energy loss from friction, the system's mechanical energy increases.

The potential energy of an object falls while its kinetic energy rises. The increase in kinetic energy exactly offsets the decrease in potential energy. The idea of work is another crucial one.

Some kinetic energy is converted into heat energy when friction occurs between two surfaces that are moving over one another.

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16.14° is the angle of refraction of the light when it leaves the glass.

Snell's law states that the angle of refraction, θr, is proportional to the angle of incidence, θi and the ratio of the refractive indices of the two media that comprise the interface. The angle θr=θi and no refraction occur when the mediums have equal refractive indices.

Given that,

The glass has an index of refraction (n₁) = 1.52

Air has an index of refraction (n₂) = 1.000293.

According to Snell's law:

n₂/n₁ = sin θ₁ / sin θ₂

or, 1.000293 / 1.52 = sin θ₁ / sin (25°)

or, 0.6581 = sin θ₁ / 0.42262

or, 0.2781 = sin θ₁

or, θ₁ = sin⁻¹ (0.2781)

or, θ₁ = 16.15°

So, 16.15° is the angle of refraction of the light when it leaves the glass.

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The magnitude-axis direction relative to the positive direction of the x axis of the dipole’s electric field at point P, located at distance r >> d is 1 / 4λεο x qd/r³.

Electric field is defined as the physical field that surrounds electrically charged particles and acts as an attractor or repellent on all other charged particles in the field. A vector quantity called an electric field can be represented by arrows pointing in the direction of or away from charges.

| E net | = 2 E sinθ = 2[1 / 4λεο x q / (d/2)² + 1³] d/2 / √(d/2)² + r ²

            = [1 / 4λεο x qd / [(d/2)² + r²] ³/²

For r >> d [(d/2)² + r²] ³/² ≅ r

So the expression will be

| E net | = 1 / 4λεο x qd / r³

Thus, the magnitude-axis direction relative to the positive direction of the x axis of the dipole’s electric field at point P, located at distance r >> d is 1 / 4λεο x qd/r³.

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The displacement of the runner after four seconds is 78.4 m.

We know that in this case, we are dealing with a case of an object that has a motion under gravity. We are told that the road runner an fell straight down off a cliff. The fact that we have been told that the runner just fell down the cliff means that the initial velocity of the runner would have to be taken in this context as zero since the runner was dropped from a height as shown.

Acceleration of the runner (g) = 9.8 m/s^2

Initial velocity of the runner (u) = 0 m/s

Time take (t) = 4 seconds

We then have;

h = ut + 1/2gt^2

If we then know that the initial velocity of the person is zero, then we have;

h = 1/2gt^2

h = 0.5 * 9.8 * (4)^2

h = 78.4 m

The height is 78.4 m.

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A cart at the end of a spring undergoes simple harmonic motion of amplitude A = 10 cm and frequency 5.0 Hz. Assume that the cart is at x = −A when t = 0.

(a) T = 0.2 sec

(b) x(t) = − (10 cm)cos(10π) s⁻¹ t

(c) x(0.050) = 0

(d) x(0.100) = 10 cm

Simple harmonic motion is described as the periodic movement of a point down a straight line with an acceleration that is always toward a fixed point on that line and is proportional to that point's distance from the moving point.

Given that,

frequency (f) = 5.0 Hz

Amplitude (A) = 10 cm

(a) As we know,

T = 1/f

or, T = 1/5 Hz

or, T = 0.2 sec

(b) Because the expression for the cart position is at  x= −A when t=0 , this means that the function which describes the position of the cart is a cosine function because, cos(0)=1.

Notice that the form of the equation that describes the position of a vibrating object is as follows :

x(t) = A cos (2Π/T) × t

Substitute for the values of T=0.2s ; A=10 cm and because x = −A when t = 0,then the function will have a negative sign

x(t) = −(10 cm)cos(10π) s⁻¹ t

(c) the position of the cart at 0.050 s:

x(0.050) = −(10 cm)cos(10π) s⁻¹ × (0.050)

x(0.050) = −(10 cm) (cos π/2)

x(0.050) = 0

(d) the position of the cart at 0.100 s:

x(0.100) = −(10 cm)cos(10π) s⁻¹ × (0.100)

x(0.100) = −(10 cm) (cos π)

x(0.100) = 10 cm

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The disk is equivalent to a solid cylinder 0.700 cm high and 3.80 cm in diameter. The shear deformation is .∆x=3.34×10⁻⁶ m.

Deformation refers to the change in size or shape of and object whereas displacements are the absolute change in to the  position of a point on the  the object. Deflections is the relative changes in external displacements in an object.

The shear deformation is .

Given that,

Shearing force F = 600 nm

Shear modulus S=1×10⁹ n/m²

length = 0.700 cm

diameter = 4.00 cm

We need to find the shear deformation

Using formula of shear modulus

S=Flo/A ∆x

∆x=Flo/(rd²/4)S

∆x=4Flo/(rd²/)S

Put the value into the formula

∆x=4×600×0.700×10²/3.14×1×10⁹×(4.00×10²)

∆x=3.34×10⁻⁶ m

Hence, The shear deformation is .∆x=3.34×10⁻⁶m

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The mass of M₂ = 12kg.

Newton's second law of motion states that an object's acceleration is equal to its mass divided by the net force acting on it, or a = F m. When an object's mass and the net force acting on it are known, this equation for acceleration can be used to determine the object's acceleration.

The formal formulation of Newton's second law is as follows: The acceleration of an object caused by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

F = ma

F = 6×4.9

F = 29.4N.

F = (M₂ - M₁)a

29.4 = (M₂- 6) 4.9

29.4/ 4.9 = M₂- 6

M₂ = 6+6

M₂ = 12kg.

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Answer: 4+5z (x) + 9

Explanation:

So I got this by... I don't really know, but this might be the right answer..

The tangential acceleration and length of chain of rocket is 0.5708 and 9.4m respectively.

Initial angular velocity, w = 65rpm = 65(rad/s = 6.594rad/s

Final angular velocity, w = 91rpm = 91(rad/s = 9.734rad/s

time taken, t= 11s

Then let total radians covered in this much time be 0 and angular acceleration be a, using equations of motion.

a). 9.734 6.59  and 0.2854rad/s

= (9.734)(6.594) +2(0.2854)/3

A=0.5708

b).Then radius of sprocket R= diameter/2= (25/2)cm E =12.5cm

Then length of chain passes over the top of sprocket in this intervalis

r= (0-12.5m)(89/ 821)

r=9.4m

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There are three general types of spectra: continuous, emission, and absorption. The image drag are:

Continuous

Image 1 (full spectrum)

Emission

Image  2 (mostly dark)

Image 5 (mostly dark)

Absorption

Image 3 (full with lines)

Image 4 (full with lines)

The distribution of light's wavelengths (or colors) differs for each type of spectrum. While the emission spectra only display individual lines of emitted color, the continuous spectrum displays a continuum of all hues. Only tiny black ranges where particular colors have been taken away are seen in the absorption spectrum.

From the image attached:

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Answer: total distance traveled = 6.5 m

Explanation:

Important to note the difference between displacement and distance.  Distance is the total length of the path taken:  4 + 2.5 = 6.5 m

Displacement is the distance from the point of origin to the ending point:

4 - 2.5 = 1.5 m

The question asked for the DISTANCE, so the answer is 6.5 m

The radius of the brass is determined as 0.091 cm.

The radius of the brass is calculated by applying the equation for the circumference of a circle.

Mathematically, the equation for the circumference of a circle is given as;

C = 2πr

where;

For the given number of turns of the coil and the height of the coil, the radius of the brass is calculated as follows;

( 2πr ) N = h

where;

( 2πr ) N = h

( 2πr ) ( 21 ) = 12

42πr = 12

r = 12 / 42π

r = 0.091 cm

Thus, the radius of the brass is a function of height of the brass and the number of turns of the brass.

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The spring constant (K) is 2.67n/m when 300 g mass hangs vertically from a spring.

A spring is a material that may be bent by an external force before resuming its original shape.

Now, the force required for every unit of spring extension is known as the "Spring constant." Knowing the spring constant makes it simple to calculate the amount of force needed to bend the spring.

Hooke's law states that F = -KX.

Calculations:

Given,

Mass = 300g = 0.3kg

Spring elongation = x = 11cm = 1.1m

Spring constant = k =?

Kx= mg

K = mg/x

K = (0.3 * 9.81) / 1.1m

K = 2.67n/m.

Hence, the spring constant (K) is 2.67n/m when 300 g mass hangs vertically from a spring.

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Because the mass is moving at a constant speed, its kinetic energy equals equal to zero. square of a amplitude and therefore is equal to the block's energy.

Acceleration is the rate at which an moving object's speed and direction change over time. Travel on a circle increases irrespective of whether the speed stays the same since its orientation is always changing.

The three main types of accelerated motions are regular acceleration, non-uniform acceleration, or average acceleration. The motion in which an item moves inside a straight line while increasing in velocity at regular intervals is referred to as uniform acceleration.

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2.2 hours long will it take them to be 330 miles apart.

They are separating at (72+76) = 148 miles per hour relative to each other, so they will take (330miles/148miles per hour)

[tex]330/148=2.2[/tex]

What are the distance problems?

Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time. Things to watch out for: Make sure that you change the units when necessary.

How do you solve distance-time problems?

To work out speed, divide the distance of the journey by the time it took to travel, so speed = distance divided by time. To calculate time, divide the distance by speed. To get the distance, multiply the speed by time. You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.

Thus, it takes 2.2 hours for them to be 330 miles apart.

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With the knowledge of differential calculus, the magnitude of the object's acceleration is 11.4 m/s²

Position is any point of coordinate in space or any region in which an object can be located.

Given that the position , in meters, of an object moving along the x-axis is given as a function of time t, in seconds, as

x(t) = 0.09814[tex]t^{4}[/tex] − 0.1953t³ + 0.8552t² + 3.15t − 7.49

The object's acceleration at time =3.41 s can be found with the knowledge of differential calculus.

The derivative of position = velocity

The derivative of velocity = acceleration

That is,

If x(t) = 0.09814[tex]t^{4}[/tex] − 0.1953t³ + 0.8552t² + 3.15t − 7.49

dx/dt = 0.39256t³ - 0.5859t² + 1.7104t + 3.15 = v

dv/dt = 1.17768t² - 1.1718t + 1.7104

when time t = 3.41 s

Substitute for t

dv/dt = a = 1.17768(3.41)² - 1.1718(3.41) + 1.7104

a = 13.69 - 4.00 + 1.7104

a = 11.4 m/s²

Therefore, the object's acceleration at time = 3.41 s, is 11.4 m/s² approximately.

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At the center of buoyancy, the buoyant force operates in an upward, vertical direction.

Here are a few real-world instances of the buoyant force. Iceberg drifting on the sea, a boat traveling down a river An individual wearing a life jacket floating in the water, a ship sailing the seas, a helium balloon soaring into the sky, etc. The density has a direct relationship with the buoyant force.

The fluid's pressure on the object is what creates the buoyant force. The net upward force results from the fact that the pressure on the bottom of an item is always greater than the force on the top since pressure rises as depth increases. Whether an object sinks or floats, the buoyant force always exists.

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Here in this scenario, this image is an example of Newton's first Law of Motion.

What is newton's law of motion?

The three fundamental laws of classical mechanics known as Newton's laws of motion describe how an object's motion and the forces acting on it interact. The following is a paraphrasing of these laws:

Isaac Newton first identified the three laws of motion in his 1687 book Philosophies Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).

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The pressure exerted on the floor by each leg is 427832.0079 Pa.

F = mg

F = (4.5 + 65) × 9.8

F= 681.1 N

This force is evenly distributed on the three leg

radius, r = d/2

= 2.6 / 2

= 1.3 cm = 0.013 m

Total cross sectional area of the three legs, A = 3×π×[tex]r^{2}[/tex]

A = 3 × 3.14 × [tex]0.013^{2}[/tex]

A = 0.00159 [tex]m^{2}[/tex]

Pressure due to weight,

P = Weight/A

P = 681.1/ 0.00159

P = 427832.0079 Pa

Hence, the pressure exerted on the floor by each leg is 427832.0079 Pa.

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Answer: The only way for the object to change its motion is if an external unbalanced force acts on it.

Explanation:

Newton's First Law of Motion (aka Law of Inertia) states:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Velocity is a VECTOR, so it has both magnitude (size) and direction.  The magnitude of the velocity of an object in motion (its speed) can stay the same, but if it changes direction, its velocity has changed.  The only way for the object to change its direction of motion is if an external unbalanced force acts on it.

The negative acceleration and distance is 451.42m/s² and 175.55m.

When an object experiences negative acceleration, its velocity changes in a negative direction, which can indicate that it is moving either slower or faster.

As a vector quantity that denotes both magnitude and direction, the term "acceleration" is used in physics to describe a change in an object's velocity.

Positive velocity, which is also a vector, makes something move more slowly than something experiencing negative acceleration. An object that has both negative acceleration and velocity, however, is actually moving faster.

a]. Negative Acceleration = dv/dt

 a=632/1.40=451.42m/s²

b]. distance= speed x time

d=632x 5/18=175.55m

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Answer: C. A hot non-polar substance

Explanation: I am guessing you have options for this, because I've already had this question at school. So C.

Box A of mass m sits on the floor of an elevator with box B of mass 2 m on top of it, in this case option b) would be correct in order of increasing magnitude.

What is magnitude?

Magnitude is a term used in physics to describe an object's maximal size and direction. Scalar and vector quantities both use magnitude as a common factor. We are aware that scalar quantities are those that have just magnitude by definition. Those quantities with both magnitude and direction are considered vector quantities.

There are different ways in which magnitude can be used. Some of them are:

An earthquake's size is measured in terms of its length, breadth, and width. It is calculated based on the earthquake's actual size. A single magnitude is thought to exist for an earthquake. Due to variables including the type of surface material and distance from the epicentre, the magnitude of the shaking brought on by the earthquake varies depending on where it occurs.

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It is given that,

Cube Length (L) = 0.29m

Density of Cube (Pc) = 0.89 *103 Kg/m3

Density of Liquid (P1) = 1.5 *103 Kg/m3

Distance (d) =?

We know that,

d = {(P1 - Pc)/P1}*L

d = {(1.5*103–0.89*103)/1.5*103}* 0.29

d = {(1.5 – 0.89)/1.5} * 0.29

d = 0.118m

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The expression to find distance using the given quantities is:

d = ( ρl - ρc ) L / ρl  

In this question, it is given that a cube with length L= 0.29 meter and the density of cube ρc = 0.89×103 kg/m3 and it floats in equilibrium in liquid of density  ρl = 1.5×103 kg/m3 with the top of the cube a distance d above the liquid surface. So here is the liquid, and the cube will float on the liquid at a distance d. Thus, the expression in terms of the given quantities to find distance d can be written as-

d = ( ρl - ρc ) L/ρl  

We are given that,

Density of cube, ρc = 0.89×103 kg/[tex]m^{3}[/tex]

Density of liquid, ρl = 1.5×103 kg/[tex]m^{3}[/tex]

Edge length of cube, L = 0.29 m

So, on substituting the given values in above expression, we get:

d = [(1.5×103 – 0.89×103) / 1.5×103] × 0.29

d = [(1.5 – 0.89) / 1.5] × 0.29

d = 0.118 m

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We can see a big truck turning right in front of you onto a roadway with two lanes going in either direction. When turning, the truck must always stay in the right lane.

Direction is characterized as the course that anything follows, the route that must be taken to reach a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you make a turn instead of left, that is an illustration of direction.

Despite taking into account compass error, the direction as shown by the instrument. The true direction referred to an Earthly meridian may vary markedly from the direction represented by a magnetic compass.

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At point P, which is situated at a distance of r >> d, the electric field of the dipole has a magnitude-axis direction that is 1 / 4 x qd/r³ in relation to the positive direction of the x axis.

The physical field that surrounds electrically charged particles and has the power to either attract or repel other charged particles in the vicinity is known as an electric field. Arrows pointing toward or away from charges can be used to depict the vector quantity known as an electric field.

| E net | = 2 E sinθ = 2[1 / 4λεο x q / (d/2)² + 1³] d/2 / √(d/2)² + r ²

            = [1 / 4λεο x qd / [(d/2)² + r²] ³/²

For r >> d [(d/2)² + r²] ³/² ≅ r

So the expression will be reduced to

| E net | = 1 / 4λεο x qd / r³

Thus, at point P, which is situated at a distance of r >> d, the electric field of the dipole has a magnitude-axis direction that is 1 / 4 x qd/r³ in relation to the positive direction of the x axis.

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