Earthquake damage causes two rabbits to be separated from the rest of the rabbits in their large habitat. They have no way to get back to their original habitat. The two rabbits mate with each other. Over time, all the offspring in the new habitat are descendants of the original two rabbits. What are the outcomes of this situation? A.The rabbits in the new habitat will have lower genetic variation than the rabbits in the original habitat. B. The rabbits in the new habitat will have a higher risk of random genetic mutations than the rabbits in the original habitat. C. The rabbits in the original habitat have a greater likelihood of choosing an unrelated mate than the rabbits in the new habitat. D.The rabbits in the original habitat will be less likely to reproduce than the rabbits in the new habitat.

Answer:

Center of Gravity is the point in a body where the gravitational force may be taken to act.  Center of Buoyancy is the center of gravity for the volume of water which a hull displaces.

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Answer:

The minimum distance to the object that the radar can detect is 124.995 m

Explanation:

Here, we are to calculate the shortest distance to an object the radar in the question can detect.

Mathematically;

v = c/λ

Where v is the frequency, c is the speed of light and λ is the wave length

Thus;

v = (3 * 10^8)/2.5 = 1.2 * 10^8 Hz

Mathematically, the time period

t = 1/v = 1/(1.2 * 10^8) = 0.000000008333 = 8.333 * 10^-9 sec

From the question, we are told that the transmitting time is 100 times a single oscillation

Transmitting time = 100 * one oscillation

Hence Transmitting time = 100 * 8.33 * 10^-9 = 8.33 * 10-7

Mathematically;

Minimum distance =( Transmitting time * speed of light)/2 =

(8.33 * 10^-7 * 3 * 10^8)/2 = 124.995 m

Answer:

a = 85.9 m / s²

Explanation:

For this exercise we can use Newton's second law in the most compressed part

             F - W = m a

force is the spring elastic force

             F = - k Δx

          k Δx - m g = m a

          a = k/m  Δx - g

         Δx = x₀ -[tex]x_{f}[/tex]

         ΔX = 46 - 5 = 41cm (1m / 100cm) = 0.41  m

let's calculate

          a = 1.4 10⁴/60 0.41 - 9.8

          a = 85.9 m / s²

Answer:

English.

Explanation:

English is undeniably accepted by scientists all over the world as the primary language of science. It is a language spoken all over the world and is also the language of science because it is an official language and can be understood by almost everyone.

Answer:

[tex]\boxed{\mathrm{English}}[/tex]

Explanation:

English is undeniably accepted by scientists all over the world as the primary language of science. The scientific methods and experiments are done by communicating and writing in English. Scientists use English to communicate and share knowledge as English is understood by people from around the world.

Answer:

Option A. 1.1×10¯²⁴ N

Explanation:

The following data were obtained from the question:

Charge 1 (q1) = - 4e

Charge 2 (q2) = + 3e

Distance apart (r) = 0.05 m

Electric field constant (K) = 9×10⁹ N•m²/C²

Electron (e) = 1.6×10¯¹⁹ C.

Electric Force (F) =..?

Next, we shall determine the value of the two charges.

This is illustrated below:

Charge 1 (q1) = - 4e

Charge 1 (- q1) = 4e

Electron (e) = 1.6×10¯¹⁹ C.

Charge 1 (- q1) = 4 × 1.6×10¯¹⁹ C.

Charge 1 (- q1) = 6.4×10¯¹⁹ C.

Charge 2 (q2) = + 3e

Electron (e) = 1.6×10¯¹⁹ C.

Charge 2 (q2) = 3 × 1.6×10¯¹⁹ C.

Charge 2 (q2) = 4.8×10¯¹⁹ C.

Finally, we shall determine the value of the electric force. This can be obtained as shown below:

Charge 1 (- q1) = 6.4×10¯¹⁹ C.

Charge 2 (q2) = 4.8×10¯¹⁹ C.

Electric field constant (K) = 9×10⁹ N•m²/C².

Distance apart (r) = 0.05 m

Electric Force (F) =..?

F = Kq1q2 /r²

F = (9×10⁹× 6.4×10¯¹⁹× 4.8×10¯¹⁹)/(0.05)²

F = 1.1×10¯²⁴ N

Therefore, the electric force between the two point charge is 1.1×10¯²⁴ N

Answer:

average speed =  66.67  km/h

Explanation:

In order to find the average speed of the train, you need to calculate the total distance traveled, divided by the time it took to cover that distance. So for the total distance:

Distance= 120 km + 180 km = 300 km

For the total time we need to add three different quantities, two of which we need to derived based on the information provided:

time for first part of the trip:

[tex]time_1=\frac{D_1}{v_1} =\frac{120}{60} \,h= 2\,h[/tex]

for the time of the stop:

[tex]time_2=0.5\,\,h[/tex]

for the last part of the trip:

[tex]time_3=\frac{180}{90} \,h= 2 \,\,h[/tex]

Which gives a total of 4.5 hours

Then, the average speed is:   300/4.5   km/h = 66.67  km/h

u=10m/s

v=15m/s

acceleration=

v_u/ t

5/10

0.5

Answer:

1.92 x 10⁻¹²J

Explanation:

The magnetic force from the magnetic field gives the circulating protons gives the particle the necessary centripetal acceleration to keep it orbiting round the circular path. And from Newton's second law of motion, the force(F) is equal to the product of the mass(m) of the proton and the centripetal acceleration(a). i.e

F = ma

Where;

a = [tex]\frac{v^2}{r}[/tex]             [v = linear velocity, r = radius of circular path]

=> F = m[tex]\frac{v^2}{r}[/tex]           ------------(i)

We also know that the magnitude of this magnetic force experienced by the moving charge (proton) in a magnetic field is given by;

F = q v B sin θ       ----------(ii)

Where;

q = charge of the particle

v = velocity of the particle

B = magnetic field

θ = the angle between the velocity and the magnetic field.

Combining equations (i) and (ii) gives

m[tex]\frac{v^2}{r}[/tex] = q v B sin θ           [θ = 90° since the proton is orbiting at the maximum orbital radius]

=> m[tex]\frac{v^2}{r}[/tex] = q v B sin 90°

=> m[tex]\frac{v^2}{r}[/tex] = q v B

Divide both side by v;

=> m[tex]\frac{v}{r}[/tex] = qB

Make v subject of the formula

v = [tex]\frac{qBr}{m}[/tex]

From the question;

B = 1.25T

m = mass of proton = 1.67 x 10⁻²⁷kg

r = 0.40m

q = charge of a proton = 1.6 x 10⁻¹⁹C

Substitute these values into equation(iii) as follows;

v = [tex]\frac{(1.6*10^{-19})(1.25)(0.4)}{(1.67*10^{-27})}[/tex]

v = 4.79 x 10⁷m/s

Now, the kinetic energy, K, is given by;

K = [tex]\frac{1}{2}[/tex]mv²

m = mass of proton

v = velocity of the proton as calculated above

K = [tex]\frac{1}{2}(1.67*10^{-27} * (4.79 * 10^7)^2 )[/tex]

K = 1.92 x 10⁻¹²J

The kinetic energy is 1.92 x 10⁻¹²J

Answer:

[tex]B=2.025\times 10^{11}\ Pa[/tex]

Explanation:

It is given that,

Speed of P- waves, v = 9 km/s = 9000 m/s

The density of rock is about [tex]2500\ kg/m^3[/tex]

We need to find the average bulk modulus of Earth's crust. Let it is given by B. So,

[tex]v=\sqrt{\dfrac{B}{d}} \\\\B=v^2d\\\\B=(9000)^2\times 2500\\\\B=2.025\times 10^{11}\ Pa[/tex]

So, the bulk modulus of the Earth's crust is [tex]2.025\times 10^{11}\ Pa[/tex].

Answer:

g, downward

Explanation:

It is given that, a baseball is thrown straight upward. The force acting on the stone is force of gravity. It is moving under the action of gravity. We know that the force of gravity always acts in a downward direction.

At the highest point, the velocity of the stone will be equal to 0. It will move will constant acceleration equal to g and it always acts in downward direction.

Hence, the correct option is (e) "downward direction".

Answer:

The light transmitted through the system will be 0.125*I₀.  

Explanation:

The light transmitted through the system can be found using Malus Law:

[tex] I = I_{0}cos^{2}(\theta) [/tex]    (1)

Where:

I: is the intensity of the light transmitted

I₀: is the initial intensity

θ is the angle relative to the first polarizer’s = 60°

Because the light transmitted by the first polarizer is dropped by half, the equation (1) results as:  

[tex] I = \frac{I_{0}}{2}cos^{2}(\theta) [/tex]

[tex] I = \frac{I_{0}}{2}cos^{2}(60) [/tex]

[tex] I = 0.125I_{0} = \frac{1}{8}I_{0} [/tex]

Therefore, the light transmitted through the system will be 0.125*I₀.  

I hope it helps you!

Answer:

C) Mitochondrial DNA

Explanation:

Mitochondrial DNA can help forensic scientists in recovering the follicular tissue that is attached to the hair, they can find out the specific suspect from that hair.

Mitochondrial DNA is maternally inherited and enables forensic scientists to trace maternal lineage.

Answer:

Mitochondrial DNA

Explanation:

Mitochondrial DNA should be used to prove that the hair in the victim's fist belonged to a specific suspect. Mitochondrial DNA enables scientists to trace maternal lineage from which it can be known that who is the suspect.

Answer:

ugmd = 1/2 kx²

d = (1/2 kx²) / (ugm)

= (1/2 * 250 N/m * (0.2 m)²) / (0.23 * 9.81 m/s² * 0.3 kg)

= 7.4 m

ugmd = 1/2 mv²

v = √2ugd

= √(2(0.23)(9.81 m/s²)(7.4 m)

= 5.8 m/s

Explanation:

The box's launch speed is 5.8 m/s.

Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.

Given in question spring with spring constant 210 Nm is compressed by 20 cm and then used to launch a 250 g box across the floor,

ugmd = 1/2 kx²

d = (1/2 kx²) / (ugm)

= (1/2 * 250 N/m * (0.2 m)²) / (0.23 * 9.81 m/s² * 0.3 kg)

= 7.4 m

ugmd = 1/2 mv²

v = √2ugd

= √(2(0.23)(9.81 m/s²)(7.4 m)

= 5.8 m/s

The box's launch speed is 5.8 m/s.

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Answer:

Time seem to flow only in one direction because if it started to go in backward direction that would break the second law of thermodynamics. We do not find time to be moving in any direction because time is not an object that can move nor is it a force that can move any object.

The amount of lighting on a surface drops to (1/4) of the initial illumination when the distance between a light source and the surface it falls on is doubled.

The amount of light or luminous flux that falls on a surface is known as illumination. It is expressed as lux or lumens per square meter.

The square of the distance has an inverse relationship with the light intensity;

[tex]\rm I = \frac{1}{r^2}[/tex]

Where,

I is the light intensity

r is the distance

Let r is the distance and I is the sound intensity for case 2;

r' = 2r

[tex]\rm I' = \frac{1}{(2r)^2} \\\\ I' = \frac{1}{4r^2} \\\\ I' = \frac{I}{4}[/tex]

When we double the distance between a source of light and the surface on which it falls, the amount of illumination on the surface decreases to(1/2) of the original illumination.

Hence the value of the fraction is 1/4.

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Answer:

Explanation:

In the decibel scale , intensity of sound changes logarithmically as follows

[tex]10log\frac{I}{I_0} =[/tex] Value in decibel scale , the value of I₀ = 10⁻¹² W /m².

Putting the values

[tex]10log\frac{I}{10^{-12}} = 71[/tex]

[tex]log\frac{I}{10^{-12}} = 7.1[/tex]

[tex]\frac{I}{10^{-12}} = 10^{7.1}[/tex]

[tex]I= 10^{-4.9}[/tex] W/m²

Similarly for 54 dB sound intensity can be given as follows

I = 10⁻¹² x [tex]10^{5.4}[/tex]

[tex]I= 10^{-6.6 }[/tex] W / m²

For intensity of sound the relation is as follows

I = 2π²υ²A²ρc where υ is frequency , A is amplitude , ρ is density of air and c is velocity of sound .

Putting the given values for 71 dB

[tex]I= 10^{-4.9}[/tex]  = 2π² x 504²xA²x 1.21 x  346

A² = 60.03 x 10⁻¹⁶

A = 7.74 x 10⁻⁸ m

For 54 dB sound

[tex]10^{-6.6}[/tex] = 2π² x 504²xA²x 1.21 x  346

A² = 1.1978 x 10⁻¹⁶

A = 1.1 x 10⁻⁸ m

Answer:

The amount of charge increases.

Explanation:

For a capacitor that has its plates still connected to a battery, the voltage on the capacitor remains constant. If the distance between the two plates of this capacitor is decreased, the capacitance will increase, and then the charge on the plate will increase in accordance with the relationship

Q =CV

From this relationship, if V is held constant, then Q has to increase for C to increase also.

Answer:

17 m/s west

Explanation:

Runner 1 has velocity = 10 m/s west

runner 2 has velocity = 7 m/s east

From the frame of reference of runner 2, we can imagine runner 2 as standing still, and runner 1 moving away from him, towards the west with their combined velocity of

velocity = 10 m/s + 7 m/s = 17 m/s west

Answer:

17 m/s west

Explanation:

Hope this helps!

Answer:

20 m

Explanation:

Given in the y direction:

Δy = 10 m

v₀ = 25 m/s sin 37° = 15.0 m/s

a = -10 m/s²

Find: t

Δy = v₀ t + ½ at²

10 m = (15.0 m/s) t + ½ (-10 m/s²) t²

10 = 15t − 5t²

2 = 3t − t²

t² − 3t + 2 = 0

(t − 1) (t − 2) = 0

t = 1 or 2

Since the projectile reaches Q before it reaches the peak, we want the lesser time, so t = 1.

Given in the x direction:

v₀ = 25 m/s cos 37° = 20.0 m/s

a = 0 m/s²

t = 1 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (20.0 m/s) (1 s) + ½ (0 m/s²) (1 s)²

Δx = 20 m

Answer:

(a) 17.0eV

(b) 10.55W

Explanation:

(a) The amount of work done (W) on an electron by an ideal battery of emf value of V as it moves from the positive to the negative terminal is given by;

W = q x V                 --------(i)

Where;

q = charge on the electron = 1e

From the question;

V = 17.0 V

Substitute the values of q and V into equation (i) as follows;

W = 1e x 17.0

W = 17.0eV

Therefore, the work done in electron volts is 17.0

(b) The power (P) of the battery as some electrons (n) pass through it at time t, is given as;

P = (n q V) / t            --------------(ii)

Where;

n = number of electrons = 3.88 x 10¹⁸

t = 1s

q = 1.6 x 10⁻¹⁹C

V = 17.0V

Substitute these values into equation (ii) as follows;

P = (3.88 x 10¹⁸ x 1.6 x 10⁻¹⁹ x 17.0) / 1

P = 10.55W

Therefore the power of the battery is 10.55W

Answer:

The wavelength is 2 meters

Explanation:

The relationship between the frequency, the speed and the wavelength is given by the relation;

v = f × λ

The given parameters are;

The distance of the duck from the edge of the pond = 12 m

The number of ripples produced per second = Frequency, f = 2 Hz

The time it takes the ripple to reach the edge of the pond after travelling past the duck = 3 seconds

Therefore, speed of the wave, v = Distance/time = 12 m/(3 s) = 4 m/s

The wavelength, λ, is therefore;

λ = v/f = (4 m/s)/(2 Hz) = 2 meters.

Explanation:

Given that,

Force, [tex]F=2i+3j-5k[/tex]

The particle displaces from (1,2,-3) m to (2,5,-1) m.

We need to find the work done by the force. Work done by the force is given by :

W = Fd

It is equal to the dot product of force and displacement.

Displacement from (1,2,-3) m to (2,5,-1) m is (2-1, 5-2, -1-(-3)) or (1, 3, 2) m

Work done,

[tex]W=F{\cdot} d\\\\W=(2i+3j-5k){\cdot} (i+3j+2k)[/tex]

We know that, i.i=j.j=k.k=1

So,

[tex]W=1\ J[/tex]

So, the work done by the force is 1 J.

Answer:

38.8 km/hr

Explanation:

The total distance is 2 × 282 km = 564 km.

The total time is 6 hr 32 min + 8 hr = 14 hr 32 min = 14.533 hr.

The average speed is:

(564 km) / (14.533 hr)

38.8 km/hr

Answer:

the mass of one sun

Explanation:

its really heavy

Answer:

The teacher should swim in a direction 29.24° North of East

Explanation:

Given that the there is a water  current across the lake, and the physics teacher intends to swim directly across the lake, the direction the physics teacher will have to swim is found as follows;

The speed of the water current is given by the speed of the floating leaf traveling with the water current  

Distance traveled by the leaf = 4.2 m South

Time of travel of the leaf = 5.0 s

Speed of leaf = 4.2/5 = 0.84 m/s = Speed of the water current

Swimming peed of the teacher, v = 1.9 m/s

To swim directly across the lake, the teacher has to swim slightly in the opposite direction of the water current, the y-component of the teacher's swimming speed should be equal to and opposite that of the speed of the water current.

Y-component of v = v×sin(θ), where θ is the angle of the direction, the teacher should swim

Therefore;

1.9 × sin(θ) = 0.84

sin(θ) = 0.84/1.9 = 0.44

θ = 26.24°

That is the teacher should swim in a direction 29.24° North of East.

To cross the lake the teacher has to swim in a direction 29.24° North of the East

The speed of the water current can be derived from the speed of the floating leaf :

The distance traveled by the leaf L = 4.2 m South

Time taken T = 5s

So, the speed of the leaf is:

u = 4.2/5

u = 0.84 m/s South

So, the speed of the current is 0.84 m/s South

Now, it is given that the speed of the teacher is, v = 1.9 m/s East

To cross the lake the speed of the teacher must be in a Northeast direction so that the North component of the speed of the teacher cancels out the speed of the current which is directed towards the South.

Let, the speed of the teacher makes an angle of θ from the EAST.

So, the North component is given by:

v(north) = vsinθ

it must be equal to the speed of the current:

vsinθ = u

1.9 × sinθ = 0.84

sinθ = 0.84/1.9

sinθ = 0.44

θ = 26.24°

The teacher should swim in a direction 29.24° North of East.

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Answer:

a)  True    b)  True

Explanation:

a) a capacitor is made up of two flat plates and each one has a charge of the same sign, therefore the statement is true

b) the current is the flow of electrons per unit of time, therefore the charge is not zero, therefore the statement is True

Answer:

0.572

Explanation:

First examine the force of friction at the slipping point where Ff = µsFN = µsmg.

the mass of the car is unknown,

The only force on the car that is not completely in the vertical direction is friction, so let us consider the sums of forces in the tangential and centerward directions.

First the tangential direction

∑Ft =Fft =mat

And then in the centerward direction ∑Fc =Ffc =mac =mv²t/r

Going back to our constant acceleration equations we see that v²t = v²ti +2at∆x = 2at πr/2

So going backwards and plugging in Ffc =m2atπr/ 2r =πmat

Ff = √(F2ft +F2fc)= matp √(1+π²)

µs = Ff /mg = at /g √(1+π²)=

1.70m/s/2 9.80 m/s² x√(1+π²)= 0.572

Answer:

Explanation:

Resistance of first wire

R₁ = ρL / A where ρ is specific resistance

for second wire the resistance

R₂ = ρ2L / A = 2 ρL / A

For third wire

R₃ = ρL /2 A

The resistance is in the order

R₂ > R₁ > R₃

So , current will be maximum in R₃

I₃ > I₁ > I₂

Where I₁ , I₂  and I₃ is current in first , second and third wire .

Answer:

34.34 °C

Explanation:

From the question,

Heat lost by the silver block = heat gained by the iron block.

cm(x-y) = c'm'(y-z)................... Equation 1

Where c = specific heat capacity of the silver block, m = mass of the silver block, c' = specific heat capacity of the iron, m' = mass of the iron. x = initial temperature of the silver block, z = initial temperature of the iron,  y = final temperature of the mixture.

make y the subject of the equation

y = (cmx+c'm'z)/(cm+c'm')............... Equation 2

Given: c = 50 g, c = 0.2350 J/g·°C, x = 100°C, m' = 50 g, c' = 0.4494 J/g.°C, z = 0°C

Substitute these values into equation 2

y = [(50×0.2350×100)+(50×0.4494×0)]/[(50×0.2350)+(50+0.4494)]

y = 1175/(11.75+22.47)

y = 1175/34.22

y = 34.34 °C