you must show all your work. a boat leaves a dock at 2 : 00 pm and travels due south at a speed of 20 km/h. another boat has been heading due east at 15 km/h and reaches the same dock at 3 : 00 pm. at what time were the two boats closest together? (12 points)

While spinning down from 500. 0 rpm to rest, a solid uniform flywheel does 5. 1 kJ of work. If the radius of the disk is 1. 2 m, its mass will be 28.33 kg

Work done = change in kinetic energy

kinetic energy = 1/2 * I * [tex]omega^{2}[/tex]

since , moment of inertia of disk = m[tex]r^{2}[/tex] / 2

kinetic energy = 1/2 *  m[tex]r^{2}[/tex] / 2  *  [tex]omega^{2}[/tex]

  5100              = 1/4 * m * [tex]1.2^{2}[/tex] * 500

mass = 28.33 kg

If the radius of the disk is 1. 2 m, its mass will be 28.33 kg

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The pressure on the bottom of the pool due to the water is 22540pa.

What is density?

A substance's density determines how closely it can be packed. The definition of it is the mass per unit volume. The formula for density is D = m/V, where D stands for density, m for mass, and V for volume, which stand in for the object's mass and volume, respectively.

What is volume?

Volume is simply the quantity of space that a three-dimensional solid occupies. One of these solids can be a cube, a cuboid, a cone, a cylinder, or a sphere.

volume of water : 10*8*2.3m³

mass of water = density of water*volume

1000 kg/ m³* 1.84 m³

184000 kg

force extracted by water on the bottom surface = mass of water xg

=184000 kg * 9.8m/s²

=1803200N

pressure : force / area

1803200N/80m²

=22540Pa

Therefore,  pressure on the bottom of the pool due to the water is 22540pa.

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The change in gravitational potential energy stored in 16 Jule.

What is gravitational potential energy?

gravitational potential energy

In classical mechanics, of the  gravitational potential at in a  location is equal to the work per unit mass that's would be needed to Move an object to that locations from a fixed references  location. It is analogous to the electric potential with the mass playing the role of charge.

Sol-As per the given question ∆PE = mgh

M= skg

g= 4m/s^2

∆h = 2m

∆PE = 2m×4m×2m

= 16 Joules.

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The total open-circuit voltage that is received is 19.41V.

Solution:

RCHP traveling in the z-direction

E = E₁₀ cos(wt - βz) + Ey₀ sin(wt - βz)

E = [tex]\sqrt{E_{y0}^{2} + E^{2} y_{0}[/tex] = [tex]\sqrt{E^{2}_{O} } +E^{2}_{O}[/tex] = [tex]\sqrt{2} .Eo[/tex]

=  [tex]\sqrt{2} Eo = 19.41 = Eo = 19.41[/tex]

Open circuit voltage is the voltage difference measured between two terminals when no current is being drawn or supplied. Short-circuit current is the current that flows when the voltage difference between terminals is forced to zero. No current flows in the circuit, but there is a voltage drop between the two points.

As a result, in an open circuit, the current through it is zero but the voltage is present. The current becomes zero and the power equals VI. When an open circuit is introduced, current flow through the circuit is interrupted. The voltage drop across each resistive element is zero when no current is flowing. However, the source potential difference appears to be open.

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It will be 10.3% (D) of a block of wood will be submerged if placed in water based on the density of wood given.

Density is the substance's mass per unit of volume. The symbol most often used for density is ρ.

How to calculate the block of wood percentage that will be submerged in water?

Density of water = 1000 kg/m³

Density of the wood = 103kg/m³

If V be the volume of the wood and x be the volume of the wood inside the water then
Vρwood*g = Vρw*g
[tex]\frac{x}{v} = \frac{103}{1000}[/tex]

Percentage of volume of the wooden block submerged in the water is
[tex]\frac{x}{v}*100 = \frac{103}{1000} * 100[/tex]
= 10.3%

So 10.3% will be the percentage of a block of wood that will be submerged if place in water, and the answer is D.

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W-weighted person standing in an escalator that is descending quickly. The person is subjected to an upward force of N from the elevator floor. (Reply N=W.)

A vehicle that travels in a mine shaft to transport people or cargo between floors of a multi - storey building is an elevator, also known as a lift. The majority of contemporary elevators are moved by electric motors through a network of cables & sheaves with the help of a counterweight (pulleys).

The word "elevator" is really the name of the a lift manufactured by a firm in the US. People began to refer to elevators as elevators since the company  was just so successful and put them in so many locations.

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Answer:

has 5 protons and the atomic numb is 5

Explanation:

atomic number = protons number

they're equal

Answer:An atom consists of a central nucleus that is surrounded by one or more negatively charged electrons. The nucleus is positively charged and contains one or more relatively heavy particles known as protons and neutrons.

Explanation:

Color is the term found in the electromagnetic spectrum is determined by its wavelength.

Radio waves, gamma-rays, visible light, and all the other elements of the electromagnetic spectrum are electromagnetic radiation. Electromagnetic radiation can be defined in phrases of a movement of mass-much less particles, called photons, each visiting in a wave-like pattern at the velocity of light.

Wavelength is the space from one point on a wave to the same point on the subsequent wave. Frequency is the range of waves that skip through a factor in a 2d. Chemistry Interaction of light with count number.

The wavelength of light is an essential property for it's miles this that determines the character of the light. pink light has a distinctive wavelength to that of blue mild and green mild has a specific wavelength from each of them.

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A box of mass 3 kg is lifted 1. 5 m onto a shelf. The change in its gravitational potential energy is 45 Joule.

The change of gravitational potential energy is equal to the work done on the box.

ΔEp = W

Where:

ΔEp = change of gravitational potential energy

W = work done

W = F x d

Where
F = force

d = distance

From the problem,

F = 3 kg x 10 N/kg = 30 N

d = 1.5 m

Hence,

W = 30 x 1.5 = 45 Joule

Therefore, the change of the gravitational potential energy is:

ΔEp = W = 45 Joule.

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Select the rate law that best explains this reaction: Rate = k  we discovered that the dissociation of phosphonate occurs in the first order, which exhibits the linear relationship between the pressure and time.

People are only slightly to moderately toxic to phosphonates. If phosphonates are consumed, they are quickly removed from the body through feces because they are not swallowed up either by digestive system. Due to the limited likelihood that phosphonates will build up in the body, ingestion through the epidermis is similarly unlikely to be harmful.

On Earth, Jupiter, plus Saturn, scientists have found the chemical molecule phosphonate. It is made up of three hydrogen atoms and one phosphorus atom. It happens frequently on gas giants alone, when both of the atmospheres are drenched in hydrogen.

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The resultant displacement of the bullet is  1,418.6 m.

The resultant displacement of the bullet is the total displacement of the bullet obtained by resolving the displacement into x and y component.

the horizontal component of the displacement (x)  = d cosθ

the vertical component of the displacement (y) = d sinθ

where;

For the first displacement;

x = 850 m x cos(0) = 850 m

y = 850 m x sin(0) = 0

For the second displacement;

x = 640 m  x   cos(36) = 517.8 m

y = 640 m  x  sin(36) = 376.2 m

Net horizontal and vertical displacement;

∑x = 850 m  +   517.8 m   = 1,367.8 m

∑y = 376.2 m + 0 = 376.2 m

The resultant displacement of the bullet is calculated as;

d = √(∑x² + ∑y²)

d = √(1,367.8²   +    376.2²)

d = 1,418.6 m

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As she crosses the highest point of her motion, the person appears to weigh 460 N.

In physics, an object's apparent weight, which reflects its actual weight, is a characteristic. When an object's force of gravity is not counterbalanced by a normal force that is equal to but opposed to it, the apparent weight of the object will differ from the actual weight of the object. An object's weight is equal to the strength of the gravitational force pulling on it by definition.

Given,

The radius of the wheel, r = 5.0 m

Time, t = 8.0 s

And the weight of the person, W = 670 N

The following formula is used to determine the person's apparent weight as she crosses the highest point of her motion:

R=m(g-a)

Let the mass of the person is,

m=W/g

m=670/9.8

m=68.37kg

Now, we have to calculate the acceleration of a person,

a=(ω²)r

a=((1rev/8s)×(2Πrad/1rev))×5m

a=3.08 m/s²

Therefore, the apparent weight is calculated as follows:

R=68.37(9.8=3.08)

R=460N

As a result, the person appears to weigh 460 N as she crosses the highest point of her motion.

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The internal Normal force is equal to

The internal Shear force is equal to

Moments at points between C and D is

Internal Normal force :

The normal force at any section of a structure is defined as the algebraic sum of the axial forces acting on either side of the section.

Shear force:

The shearing force (SF) is defined as the algebraic sum of all the transverse forces acting on either side of the section of a beam.

Bending moment

The bending moment (BM) is defined as the algebraic sum of all the forces’ moments acting on either side of the section of a beam.

let Ax and Ay be horizontal and vertical component of A .

we have given that W₁ = 200 N/m × 6 m = 1200 N

and W₂ = 1/2 × 200 N/m× 6m = 600 N ( for triangle)

the distance between B and W₂ (x₂) = 1/3×6 = 2m

the distance between B and C (x₁) = 1/2×6 = 3m

Forces act in horizontal direction (Fₓ) ,

summation Fₓ = 0 = > Aₓ= 0

now, for vertical direction as Ay act upward and W1 and W2 acting downward direction.

summation M = 0

=> - Ay × 6 + W₁× 3 + W₂× 2 = 0

=>- 6Ay + 3600 N-m + 1200 N-m = 0

=> -Ay× 6 = - 4800 => Ay = 800 Nm

As we know total sum of force acting free body

= 0

=> Aₓ + N꜀ = 0 where N꜀ is normal force on C

but Ax= 0 so, Nc = 0

for Shear forces , Summation Fy = 0

=> Ay - W₁ - W₂ - V꜀ = 0 , where V꜀ is shear force

V꜀ = 800 - 200× 3 - 200 × 3/2 = -100 N

sum of moments Mc = 0

=> M꜀ - Ay ×3 - W1 × 3/2 - W2×1/3 ×3 = 0

=> M꜀ - 2400 - 1200× 3/2 - 600 × 1 = 0

=> M꜀ = 4.8 kNm

Hence , Internal Normal force is zero

shear force is 100 N and moment of force between C and D is 4.8 kNm.

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The angle at which a ray of light strikes a pane of window also called angle of incidence is always equal to the angle of reflection i.e. the angle at which it passes out the other side.

What is angle of incidence?

In Physics, on a plane mirror, there is a point of incidence at which the ray of light falls and returns to the same medium after reflection along the normal. as a result of this, an angle is formed which is called angle of reflection. While the angle formed between the normal point and the incident point is called angle of incidence.

Simply put, angle of reflection and angle of incidence are equal to each other.

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The height between high tide and low tide is referred to as the tidal range. tides are the peaks and valleys in sea levels brought on by the gravitational pull of the Moon, Sun, and Earth's rotation.

Tidal range is influenced by time and place. When the gravitational pulls of the Moon and Sun are in harmony, spring tides (spring range) occur, which have a larger tidal range. 0.6 metres (2 feet) is the average tidal range in the open ocean (blue and green on the map on the right). This range increases significantly closer to the coast at gravitational, there are several different coastal tidal ranges that range from almost zero to over 16 metres (52 ft).

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The color spectrum emitted by the bulb as the resistance of the circuit is increased is red.

Rt - Ro =  1 + α ΔT

Rt = Final resistance

Ro = Initial resistance

α = Coefficient of resistivity

ΔT = Change in temperature

Rt - Ro ∝ ΔT

Therefore, resistance is directly proportional to temperature.

As resistance increase, temperature also increases. As temperature increase, the molecules will vibrate faster and the wavelength will be shorter and the frequency will be higher. Since red has the shortest wavelength in the visible spectrum, the bulb will appear red.

Therefore, the color spectrum emitted by the bulb as the resistance of the circuit is increased is red.

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Answer: velocity

Explanation:

Your slope is calculated as [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{displacement}{time}[/tex], which equals velocity.

The torque on the beam calculated from the principle of moments is 68 N to the right.

The torque on the beam is calculated using the principle of moments.

The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments about a fixed point for a system in equilibrium.

Moment = force * perpendicular distance from the fulcrum

Taking the left end of the beam as the anticlockwise direction ad the right end of the beam as the clockwise direction:

Anticlockwise moment = F * (0.75 - 0.25)

Where F is the balancing force

Anticlockwise moment = 0.5f

Clockwise moment = (0.77 * 9.8) * (0.75 - 0.3)

Clockwise moment = 34 J

0.5 F = 34

F = 68 N

Hence, torque is 68 N

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To learn the acceleration and velocity to find the solution.

What is acceleration?

The rate at which the speed and direction of a moving object change over time is known as acceleration. Any movement, whether straighter, faster, or slower, is referred to as acceleration. The fact that the direction is constantly shifting causes motion on a circle to accelerate even though the speed is constant.

What is velocity?

The velocity of a body or object determines the direction of its motion. Speed is often measured as a scalar value. The most basic definition of a vector quantity is velocity. It gauges the rate at which a distance varies. It relates to the speed at which displacement is altering.

Initial height = 6ft

initial velocity v₀= 41i+3gj+27k

assume upwards, as +k acceleration

due to gravity= -9.8m/s²k or

=-32ft/s² k

initial height (s₀)= 6k

position of the ball, after t secs

s= s₀+v₀t+1/2a₀t²

s=6k+(41i+3gj+27k) t+1/2(-32k)t²

r(t)=s=41 i+3gtj +(27t-16t²=6)k ⇒ 1

If the ball is catch by a player 6A above ground

s=6k

so comparing with equation 1

6=27t-16t²+6⇒ t(27-16t)=0

t=0 and t=27/6k =1.6875sec

at t=1.6875sec

from equation 1 r(1.675)=s=69.1815i+65.8125j+6k

so( 69.1875, 65.8125,6)

So he is in bound after he catches the ball.

Therefore,  he is in bound after he catches the ball.

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Answer: -8.66 m/s2 (down)

Explanation:

Find the mass of the boulder:

F = ma

m=F/a = -3125N/9.8 m/s2 = 325 kg

F net = -3125 N + 370 N = -2815 N

now you can find a:

a = F/m = -2185 N / 325 kg = -8.66 m/s2

2.a) The two reason of using isotope of gamma radiation over  isotope of alpha radiation is:

b) i)  According to the graph, the radioactive isotope remains inside left kidney for a long time period and it comes out from right kidney after some time.

ii) Only right kidney works properly because in left kidney the radioactive material remains for a long time which is not natural.

c) i) half life time of a radioactive material is a time in what the material decays into half.

ii) Short half life means the radioactivity of the material remains for short time which is less harmful for patient. So, doctor use it.

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The size of the field needed to create resonance is

= [tex]2\pi fmp/q[/tex]

= [tex]2\pi (12.0X10[/tex]⁶)([tex]1.67X10[/tex]⁻²⁷kg)

= 0.787T.

What is Kinetic energy?

A particle or an item that is in motion has a sort of energy called kinetic energy. When work, which entails the transmission of energy, is done on an object by applying a net force, that object acquires kinetic energy.

Therefore, the Kinetic energy is given by

K = 1/2 mv²

  = 1/2m[tex](2\pi Rf)[/tex]²

 = 1/2[tex](1.67X10[/tex]⁻²⁷kg)4[tex]\pi[/tex]²(0.530m)²(12.0X10⁶Hz)²

 = 1.33X10⁻12J

 = 8.34X10⁶eV.

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Answer:The first major problem Watney faces is getting stranded and wounded on Mars. The second problem Watney faces is how he is going to survive on mars till help can come. The final problem he faces is how is he going to get to the Ares, so he can leave Mars.

Explanation: I'm not too sure if this was what u were talking about but hope it helps!

The joules carrier by an electron volt will be = 1.602 x 10-19 J

What do you mean by electric potential?

Electric potential can be defined as  the amount of work which is needed to move an unit charge from a reference point to a specific point against an electric field.

It can be calculated by the given formula

V=kQ/r or V = k Q / r . It  is a scalar quantity while the electric field is a vector.

Uses of Electric Potential.

Hence, in the above question the joules carrier by an electron volt will be = 1.602 x 10-19 J.

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The percentage error of Jocelyn's estimate is 2.135%

Estimated measurement of wood by Jocelyn = 5.5 cm

Actual measurement of wood = 5.62 cm

error value in calculation = 5.62-5.5 = 0.12 cm

Percentage error = (estimated number - actual number) / (actual number) * 100 = (0.12/5.62)*100

= 2.135 %

What is percentage-

% in mathematics is a quantity or ratio that is stated as a fraction of 100  Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it lacks dimensions and has no associated unit of measurement.

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A sarcomere will produce its greatest amount of active force at a resting size of 1. 7 um rather than 2. 15 um.

Sarcomeres are referred to as the basic contractile unit or muscle fiber. The two main protein filaments that make up each sarcomere and are responsible for triggering muscle contraction are myosin and actin. The most popular idea cited to explain how muscles contract is the hypodermic needle theory.

The Function of Sarcomeres

Muscle cells can be observed to have stripes-like striations under a microscope. This pattern is made up of a collection of basic muscle tissue units called sarcomeres that are stacked one on top of the other.

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The speed of ball when the catcher catches it is 120km/h.

Speed is the rate of change of displacement with respect to time.

In this case, if the acceleration is constant, use the third equation of motion to determine the initial and final velocities.

The third equation of motion is

v² - u² = 2gS

where v---> final velocity

u---> initial velocity

g---> gravitational acceleration

S---> height

Given Data:

Initial Velocity of the Ball (u) = 120 km/h

Initially the ball is moving up, so the acceleration of the ball is g = - 9.81 m/s²

The final velocity of the ball is v = 0 m/s

The height of the ball above the ground can be calculated by using above formula

0 - (120×5/18 m/s)^2 = 2× (-9.81 m /s²) × S

=> S = 56.7 m

When the ball is above the hit point, the initial velocity of the ball at this point is u = 0 m/s.

Using above relation we can calculate the final velocity,

56.7 × 2 × (9.81) = v²-0 = v²

=> v² = 1112.45 m/ s => v= 33.45 m/ s

or v = 120 km/h.

Therefore the velocity of the ball when caught by the catcher is 120 km/h.

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Magnetic field - You would need N = 3032 of wire.

What is a magnetic field?

The magnetic influence on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it when the charge is traveling through a magnetic field.

As seen in the following equation, a solenoid's magnetic field is
B = μ₀ n I

where n is the turn density, I is current and has a permittivity in a vacuum of 4 107 N/A2.

Let's use this equation to solve the issue; in this case, the length of the magnet is the unit of length, and the turn density is the number of turns per unit length.

L = 8 cm = 0.08 m
Let's compute.
B = μ₀ N/L I
N = B L / μ₀ I
N = 0.10 0.08 / (4π 10⁻⁷ 2.1)
3,032 103 turns,

Hence, the number of turns is 3032.
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The train's displacement from point A when it reaches point C = 1800m

The train's displacement from point A when it reaches point B =1800m

The train accelerate each time its speed change =1 m/s² and -0.5 m/s²

a.  Plot of graph is mentioned in the image .

b.  Now from the plot -

[tex]Area \\of\\Triangle = [ base * height ]/2\\[/tex]                                                                                  

[tex]S= [ 20 *20 +60*20 +40*20 ]/2 = 1800 m[/tex]

These are the sums of the areas on the graph from t=0 to t=120.

     2. Since the train was at rest from point C till point B, the displacement remains the same -

S=1800m

     3.  To  calculate the value of acceleration:-

[tex]0 < t < 20 ---------- > a= 20m/s / 20 s =1m/s^{2} \\[/tex]

[tex]80 < t < 120-------- > a=-20ms^-1/40s =-0.5m/s^{2}[/tex]

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