A student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an angle of 30 degrees with the horizontal. To make his job easier, he oiled the bottom of the box, reducing the coefficient of friction to 0.250. What is the magnitude of the acceleration of the box?

Explanation:

Given that

             [tex]rA(t)=(3.00 m/s)t\hat{i}+ (1.00 m/s^2)t^2\hat{j}\texttt{ and }rB(t)=(4.00 m/s)t\hat{i}+ (-1.00 m/s^2)t^2\hat{j}[/tex]

We need to find distance when t = 3 s

Substituting t = 3 s

             [tex]rA(t)=(3.00 m/s)\times 3\hat{i}+ (1.00 m/s^2)\times 3^2\hat{j}=9\hat{i}+9\hat{j}\\\\rB(t)=(4.00 m/s)\times 3\hat{i}+ (-1.00 m/s^2)\times 3^2\hat{j}=12\hat{i}-9\hat{j}[/tex]

[tex]\texttt{Displacement = }12\hat{i}-9\hat{j}-(9\hat{i}+9\hat{j})=3\hat{i}-18\hat{j}[/tex]

[tex]\texttt{Magnitude = }\sqrt{3^2+(-18)^2}=18.3m[/tex]

Option C is the correct answer.

The distance between object A and object B is approximately 18.248 meters. (Choice C)

In this question we must apply the concepts of vector difference, dot product and norm to determine the distance between objects A and B, in meters:

[tex]r_{B/A} = \sqrt{(\vec r_{B}-\vec r_{A})\,\bullet\,(\vec r_{B}-\vec r_{A})}[/tex] (1)

Where:

If we know that [tex]\vec r_{A} = (3\cdot t, t^{2})\,\left[m\right][/tex], [tex]\vec r_{B} = (4\cdot t,-t^{2})\,\left[m\right][/tex] and [tex]t = 3\,s[/tex], then the distance of B relative to A is:

[tex]r_{B/A}=\sqrt{t^{2}+4\cdot t^{4}}[/tex]

[tex]r_{B/A} = t\cdot \sqrt{1+4\cdot t^{2}}[/tex]

[tex]r_{B/A} = 3\cdot \sqrt{1+4\cdot 3^{2}}[/tex]

[tex]r_{B/A} \approx 18.248\,m[/tex]

The distance between object A and object B is approximately 18.248 meters. (Choice C) [tex]\blacksquare[/tex]

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Answer: 14.62 Earth days

Explanation:

This problem can be solved by Kepler’s Third Law of Planetary motion:

[tex]T=2 \pi \sqrt{\frac{a^{3}}{GM}}[/tex]

Where:

[tex]T[/tex] is the period of the probe

[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant

[tex]M=1(10)^{13} kg[/tex] is the mass of the comet Churyumov–Gerasimenko

[tex]a=30 km \frac{1000 m}{1 km}=30000 m[/tex] is the semimajor axis of the orbit the probe described around the comet (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit)

[tex]T=2 \pi \sqrt{\frac{(30000 m)^{3}}{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(1(10)^{13} kg)}}[/tex]

[tex]T=1,263,771.768 s \frac{1 h}{3600 s} \frac{1 Earth-day}{24 h}=14.62 Earth-days[/tex]

Hence, the orbital period of the probe is 14.62 Earth days.

The orbital period of the Rosetta space probe, in orbit around the comet Churyumov–Gerasimenko in 2014, is calculated to be approximately 0.178 Earth days using Kepler's Third Law of Planetary Motion and given values.

This question pertains to the calculation of the orbital period of the Rosetta space probe when it entered orbit around the comet Churyumov–Gerasimenko in 2014. First, we establish the gravitational constant (G) as approximately 6.674 × 10^-11 m^3 kg^-1 s^-2. To calculate the orbital period of an object in orbit around a celestial body, we can use Kepler's Third Law of Planetary Motion which states the square of the orbital period T is proportional to the cube of the semi-major axis a. Rearranging this law and substituting, we get T = 2π sqrt(a^3/(G*M)). Applying the given values, we get T = 2π sqrt((30*10^3 m)^3/(6.674 × 10^-11 m^3 kg^-1 s^-2*1.0*10^13 kg)) = 15378 seconds or approximately 0.178 days.

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Answer:

If the cell is placed in a surrounding solution which is hypotonic in nature.

Then the water from outside of the cell to the inside of the cell. The water will keep on moving from the outside of the cell to the inside of the cell.

The flow of water will take place until the outside environment of the cell and the inside of the cell becomes equal.

The flow of water will take place from the outside of the cell to the inside of the cell.

Answer:

The direction of motion of water molecules will be into the cell.

Explanation:

Answer:

The center of mass of a cone is located along a line. This line is perpendicular to the base and reaches the apex. The center of mass is a distance 3/4 of the height of the cone with respect to the apex.

Explanation:

The center of mass of a solid cone is located one-third of the way up from the base.

The center of mass of a solid cone is located at one-third of its height from the base. In this case, the cone is 10 cm high, so the center of mass is located 10 cm * (1/3) = 3.33 cm from the base.

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Answer:

0.1

Explanation:

mass, m = 5 kg

θ = 60°

Force, F = 10 N

velocity is constant , it means the net force is zero.

So, the component of force along the surface is equal to the friction force

FCosθ = friction force

10 x cos 60 = μ x m x g

where, μ is the coefficient of friction

5 = μ x 5 x 9.8

μ = 0.1

Thus, the coefficient of friction is 0.1

Answer:

A. The horizontal velocity vector points to the right & equals v cos θ.

Explanation:

The motion describes a parabolic path, where the horizontal speed is constant and the horizontal velocity vector always points to the right and equals v*cos θ.

Answer:

option C

Explanation:

The correct answer is option C

An orange triangular sign on the rear of the vehicle will show that the vehicle will move at a slow speed.

Warning Sign is an important method of conveying the message. Warning sign helps for the smooth movement of the traffic.

A car with an orange sign on the rear will inform the fellow driver that the vehicle is slow and they can overtake it.

Answer:

Time taken to cover the distance 11.45 s.

Explanation:

The given parameters:

Initial Velocity(u)=24 m/s

Acceleration (a)=8 [tex]m/s^{2}[/tex]

Distance or Displacement(s)=800 m

Displacement or Distance is equal in the above because it travels in a straight line.

We have to apply Second Equation of Motion,

s=ut+[tex]\frac{1}{2} at^{2}[/tex]

800=24t + 4[tex]t^{2}[/tex]

200=6t + [tex]t^{2}[/tex]

[tex]t^{2}[/tex] + 6t - 200=0

Solving, the quadratic equation to find out the roots, we get that the possible values of t will be 11.45 s and a negative value.

The negative value will be neglected as time cannot be negative.

Hence, the time taken is 11.45 s.

Answer:

Explanation:

Given

mass of gas [tex]m=8000 gm=8 kg[/tex]

Area of Piston [tex]A=5 cm^2[/tex]

[tex]T_1=15^{\circ}C[/tex]

[tex]T_2=27^{\circ}C[/tex]

no of moles [tex]n=0.28[/tex]

Work done on the gas is given by

[tex]W=-P\Delta V[/tex]

[tex]P\Delta V[/tex] can also be written as [tex]nR\Delta T[/tex]

as PV=nRT

[tex]W=-nR\Delta T[/tex]

[tex]W=-0.28\times 8.314\times (27-15)[/tex]

[tex]W=-27.93 J[/tex]

negative sign indicates that work is done on the system i.e. surrounding done a positive work on the gas

Answer:

Tm = 1,728.38 °C

Explanation:

mass of metal forging (Mm) = 67.2 kg

specific heat capacity of metal forging (Cm) = 438 J/kg°C

initial temperature of metal forging (Tm) = ?

final equilibrium temperature (Te) = 58.3 °C

mass of oil (Mo) = 786 kg

specific heat capacity of oil (Co) = 2950 J/kg°C

temperature of oil (To) = 37.1 °C

Mm × Cf × (Tm - Te) = Mo × Co × (Te - To)

Tm = [tex]\frac{Mo x Co x (Te - To) }{Mm x Cf}[/tex] + Te

Tm = [tex]\frac{786 x 2950 x (58.3 - 37.1) }{67.2 x 438}[/tex] + 58.3

Tm = 1,728.38 °C

Answer:

Dermatome. (Ans. C).

Explanation:

Dermatome is defined as the area of the human anatomy skin which is supplied by single spinal sensory nerve root. At the spinal cord these spinal sensory nerve enter the nerve root, and the branches of spinal sensory reach to the periphery of the body.

The sensory nerve which is present in the periphery of the body are the type of nerve which helps to transmit signals from sensation such as pain, temperature, etc. to the spinal cord from some specific area of the anatomy.

Answer:

Option A.

Explanation:

In quantum physics there is a law to relate the position and the momentum of the particle, it says that if we know with precision where is a quantum particle, we can not know the momentum of this particle, in other words, the velocity of the particle. So, when we measure the velocity of the particle we find the correct value of the particle, but we can not determine with accuracy where is the particle. This law is known as the Heisenberg's uncertainty principle and, its expressed as follows:    

[tex] \Delta x \Delta p \geq \frac{h}{4 \pi} [/tex]

where Δx: is the position's uncertainty, Δp: is the momentum's uncertainty and h: is the Planck constant.  

Therefore, the correct answer is A: measuring the velocity of a tiny particle with an electromagnet has no effect on the velocity of the particle. It only affects the determination of the particle's position.      

I hope it helps you!

Answer:

a.large particles such as gravel

Explanation:

High energy environments are typically associated with larger particles such as gravel due to the ability of these environments to move larger matter. Smaller particles are generally found in lower energy environments.

High energy environments, such as fast-flowing rivers or coastal areas with strong waves, are most capable of moving larger particles. So, among these options, the environments with high energy are most likely to contain large particles such as gravel (a). The other particles listed (silt, manganese nodules, cosmogenous sediments, clay) require less energy to be moved, so they are likely to be found in lower energy environments.

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Answer:

110 cm

Explanation:

Gradpoint

Answer:

The answer is B

Explanation:

Density of the element lead (Pb) is:

[tex]d_{Pb} =11,3kg/dm^3[/tex]

Density of the element Copper (Cu) is:

[tex]d_{Cu} =7,9kg/dm^3[/tex]

First we need o find the volume of both materials:

[tex]V_{Pb}=5/11,3=440cm^3[/tex]

[tex]V_{Cu}=5/7,9=630cm^3[/tex]

And the buoyant forces on elements are:

[tex]P_{Pb}=440*1*9,81/1000=4,32N[/tex]

[tex]P_{Pb}=630*1*9,81/1000=6,18N[/tex]

Answer: the car on the right should yield to the car that arrived first. That is When the car on the left arrives first

Explanation:

It must be noted that the law did not grant the 'right-of-way'. The law only says when the right of way must be yielded. The law does state who must yield the right of way neither does the law give right of way to anyone.

Yielding the right of way to another vehicle simply means that you are letting them go before you in a traffic situation.

Therefore, When two vehicles approaches an intersection without no traffic signs or signals, (that is, an uncontrolled intersection) the two vehicles must slow down. Always Yield to vehicles already in the uncontrolled intersection and drivers who arrive at the uncontrolled intersection before you.

The vehicle on the left should always yield to the right of the way to the vehicle on the right. The driver with ''right-of-way'' must pay attention to avoid a collision.

Answer:

The frequency of the standing wave in the second case is higher than that in the first case

Explanation:

The frequency and wavelength of a wave are related.

The moment you sliced the bottle, you've reduced the wavelength of the bottle.

When wavelength decreases, frequency increases and vice versa.

So, When frequency increases in the second case, more wave crests pass a fixed point each second. That means the wavelength shortens. So, as frequency increases, wavelength decreases. The opposite is also true—as frequency decreases, wavelength increases.

Answer:

The magnitude of the flux is  [tex]2.00 N m^2/C[/tex]

Explanation:

The electric flux through a planar area is defined as the product of electric field and the  component of the area perpendicular to the field.

Electric flux = Electric field * Area * (angle between the planar area and the electric flux)

The equation is

[tex]\phi = E A cos(\theta)[/tex]

Where:

[tex]\phi[/tex]is the Electric Flux

A is the  Area

E is the Electric field

[tex]\theta[/tex] is  angle between a perpendicular vector to the area and the electric field

Now substituting the values,

[tex]\phi = 5.00 \times 4.00 \times cos(0)[/tex]

[tex]\phi = 5.00 \times 4.00 \times 1[/tex]

[tex]\phi = 2.00 N m^2/C[/tex]

The flux of a constant electric field in the z-direction through a rectangle in the xy-plane is zero, because the angle between the direction of the electric field and the direction of the normal to the area is 90 degrees, which makes the dot product zero.

To calculate the magnitude of the flux of an electric field, we use the equation: Φ = E . A where Φ is the electric flux, E is the electric field, and A is the area of the surface. The dot (.) represents a dot product, which means we consider the angle between the field and the area. In this problem, the electric field (E) is given as 5.00 N/C and the area of the rectangle (A) is 4.00 m². Also, because the electric field is in the z-direction (up and down), and the rectangle is in the xy-plane (flat), the angle between the field and the area is 90 degrees.

However, the dot product for angles of 90 degrees is zero because cos(90°) = 0. So, regardless of the magnitudes of the electric field and the area, the flux is zero because Φ = E . A = EAcos(90°) = 0. Therefore, the correct answer is (a) 0.

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Answer:

Vs = 6.73 m/s or Vs = 16.3 m/s

Explanation:

frequency of the trains whistle (f) = 1.64 x 10^{2} Hz = 164 Hz

frequency of beats heard = 4 beats/s = 4 Hz

velocity of the stationary train (Vr) = 0

velocity of sound in air (V) = 343 m/s

velocity of the moving train (Vs) = ?

we can get the velocity of the moving train from the formula below

Fn = f x [tex]\frac{V + Vr}{V - Vs}[/tex] ...equation 1

where Fn = net frequency

substituting the known values into equation 1

168 =  164 x [tex]\frac{343 + 0}{343 - Vs}[/tex]

1.02 = [tex]\frac{343 + 0}{343 - Vs}[/tex]

Vs = [tex]343 - \frac{343 + 0}{1.02}[/tex]

Vs = 6.73 m/s

substituting the known values into equation 1

168 =  160 x [tex]\frac{343 + 0}{343 - Vs}[/tex]

1.05 = [tex]\frac{343 + 0}{343 - Vs}[/tex]

Vs = [tex]343 - \frac{343 + 0}{1.05}[/tex]

Vs = 16.3 m/s

Answer:

The greater force on the rope is exerted by:

C. both the same, interestingly enough

Explanation:

Answer:

equal loudness curve

Explanation:

The curves of equal loudness, first established by Munson and Fletcher in 1930 and subsequently recalculated by Robinson and Dadson, show the relationship that must exist between the frequencies and intensities (or sound pressure) of two sine sounds to be perceived equally loudly. , that is, with the same loudness.

The sinusoidal sounds contained along each curve have the same loudness. This frequency dependence would be mainly due to the transfer characteristics of the external and middle ear. It should also be noted that as the sound pressure level increases, the curves become flatter, that is, the frequency dependence is smaller as the sound pressure level increases.

The loudness level of any sound (complex) is determined by comparing its loudness with that of a sinusoidal sound.

A curve plotted as a function of frequency defining the sound pressure level required to give equal loudness is known as an equal-loudness curve. These curves use the phon unit to illustrate how different sound pressure levels are needed at various frequencies for a sound to be perceived as equally loud.

The curve plotted as a function of frequency defining the sound pressure level required to give equal loudness is known as an equal-loudness curve. These curves are critical for understanding how the human ear perceives sound at different frequencies and intensity levels, using a unit called a phon to express loudness numerically. Phons and decibels are defined to be the same at 1000 Hz, which serves as a standardized point of reference. The equal-loudness curves show that at different frequencies, different sound pressure levels are required for a sound to be perceived as equally loud. This phenomenon underlines the non-linear nature of human hearing across the frequency spectrum.

Large numbers of people have compared the loudness of sounds at different frequencies and sound intensity levels to determine these curves. Each curve is labeled with its loudness in phons, and all sounds on a given curve are perceived as equally loud. This concept is vital for various applications, including the design of audio equipment, hearing aids, and soundproofing materials, to ensure sound is produced or mitigated in a manner consistent with human loudness perception.

Explanationhe rotational kinetic energy is

[tex]K_{r} =\frac{1}{2} Iω^{2}[/tex]

The moment of inertia  I  for a sphere is  ( 2 / 5 ) m r ^2

. Substituting this in the equation yields

Kr=1/2( ( 2 / 5 ) m r ^2 )([tex](\frac{v}{r})^{2}[/tex]

1/5mv^2

1/5*5.97 × 10 ^24 *(2[tex]\pi[/tex]*6.38*10^6/86400)^2

2.57 × 10 ^29 J

b. kinetic energy of the sun

K.E=1/2*mv^2

the distance from the earth to the sun is given as

.

Answer:

a. 7.43 × 10³⁴ J b. 3.51 × 10³⁸ J

Explanation:

a. The gravitational force of attraction of a body on the surface of the earth equals the centripetal force on it due to the earth.

So, GMm/R² = mRω²

ω = √(GM/R³) where ω = angular speed of the earth. M = mass of earth = 5.972 × 10²⁴ kg, R = radius of earth = 6.4 × 10⁶ m and G = gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg²

The rotational kinetic energy of earth K.E = 1/2Iω² where I = rotational inertia = 2/5MR²

K.E = 1/2Iω²

= 1/2 × 2/5MR² × GM/R³

= GM²/5R

= 6.67 × 10⁻¹¹ Nm²/kg² × (5.972 × 10²⁴ kg)² /(6.4 × 10⁶ m × 5)

= 7.43 × 10³⁴ J

b. Similarly, the rotational kinetic energy of the earth around the sun is

K.E = GM²/5R where M = mass of sun = 1.989 × 10³⁰ kg and R = distance of earth from sun = 1.5047 × 10¹¹ m

K.E = GM²/5R

= 6.67 × 10⁻¹¹ Nm²/kg² × (1.989 × 10³⁰ kg)² / (1.5047 × 10¹¹ m × 5)

= 3.5073 × 10³⁸ J ≅ 3.51 × 10³⁸ J

Answer:

If the stone is thrown from the ground, the correct answer is A. If it is thrown from a height h, the correct answer is D.

Explanation:

Hi there!

I can´t see the drawing but let´s assume that initially, the stone is on the ground level. If that is the case, initially, the potential energy will be zero and when it returns to Earth it will also be zero. The potential energy depends on the height of the stone. If the final and initial height of the stone is zero, then the change in potential energy will also be zero:

ΔPE = final PE - initial PE

ΔPE = m · g · hf - m · g · hi (where hf and hi are the final and initial height respectively)

ΔPE = m · g (hf - hi)

ΔPE = m · g (0)

ΔPE = 0

Initially, the kinetic energy (KE) of the stone is the following:

KE = 1/2 · m · v0²

As the stone goes up, the kinetic energy is transformed into potential energy; but as the stone starts to fall, the acquired potential energy is transformed again into kinetic energy, so that the final and initial kinetic energy of the stone is the same.

Then:

ΔKE = final KE - initial KE = 0 (because final KE = initial KE).

Then, the correct answer is A.

Always ΔKE = -ΔPE due to the conservation of energy. Potential energy can´t be acquired by the stone if there is no loss of kinetic energy and vice-versa.

Let´s assume now that the stone is thrown from a height hi to the ground.

The final potential energy will be zero (becuase h = 0) but the initial PE will be:

PE = m · g · h1

Then:

ΔPE = final PE - initial PE = 0 - m · g · h1

Then ΔPE will be negative.

The initial kinetic energy will be:

KE = 1/2 · m · v0²

But the final kinetic energy will be equal to the initial kinetic energy plus the loss of potential energy (remember: if potential energy decreases, another type of energy has to increase, in this case, kinetic energy and vice-versa):

ΔKE = final KE - initial KE

ΔKE = 1/2 · m · v0² + m · g · h1 - 1/2 · m · v0²

ΔKE = m · g · h1

Then ΔKE will be positive and the correct answer would be D.

Answer:

B) The cosmic background radiation is expected to contain spectral lines of hydrogen and helium, and it does.

Explanation:

Answer:

this description is valid for mediadle displacement, bone is an acceptable description

Explanation:

The description of a person's position must be done with a position vector. These vectors must have magnitude, a given direction and a starting point.

In the description this has a starting point corner NO of pine and 675.

Each displacement occurs with respect to the previous one, indicating the magnitude of the displacement and its direction.

After analyzing  this description is valid for mediadle displacement, bone is an acceptable description

Answer:

The ball's initial kinetic energy

The ball comes to a stop at B. At this point its initial kinetic energy is converted into potential energy

Explanation:

A ball is fixed to the end of a string, which is attached to the ceiling at point P. As the drawing shows, the ball is projected downward at A with the launch speed v0. Traveling on a circular path, the ball comes to a halt at point B. What enables the ball to reach point B, which is above point A? Ignore friction and air resistance.

From conservation of energy which states that energy can neither be created nor be destroyed, but can be transformed from one form to another.

Ki+Ui=Kf+Uf

Ki=initial kinetic energy

Ui=initial potential energy

Kf=final kinetic energy

Uf=final potential energy

we know that [tex]\frac{1}{2} mu^{2} +mgha=\frac{1}{2} mv^{2} +mghb[/tex]

m=mass of the ball

ha=downward height a

hb=upward height b

u=initial velocity u

v=final velocity v, which is 0

g=acceleration due to gravity

v=0 at final velocity

1/2mu^2+mgha=0+1/2mv^2

ha=hb+Ki/mh

From the above equation, we can conclude that the ball's initial kinetic energy  is responsible for making the ball reach point B.

Point B is higher than point A from the motion gained by the ball

Answer:

Answer Choose “Faster response” in the sampling pull-down menu

Explanation:

At the top of the report, below the date range selector, select faster response,

This option uses a smaller sampling size to give you faster results. In order to get a better understanding lets define sampling, according to Google analytics website  

In data analysis, sampling is the practice of analyzing a subset of all data in order to uncover the meaningful information in the larger data set.  

For example, if you wanted to estimate the number of trees in a 100-acre area where the distribution of trees was fairly uniform, you could count the number of trees in 1 acre and multiply by 100, or count the trees in a half acre and multiply by 200 to get an accurate representation of the entire 100 acres.

To speed up Go_ogle Analytics reports, you can reduce the date range and complexity of the report, or increase server resources.

To increase the speed at which Go_ogle Analytics compiles reports, several actions could be taken. First, one can reduce the amount of data that is being processed by adjusting the date range of the reports. By analyzing a smaller chunk of data, the report can be generated much faster.

Secondly, one can adjust the complexity of the report. The more complex the report, the more data needs to be processed, hence it will take longer. Reducing the complexity and only focusing on the key metrics can help speed up the report compilation.

Lastly, one can increase the capacity of their server resources. If a company has the means, it can invest in dedicated server resources for Go_ogle Analytics, allowing it to process reports faster.

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Answer:

1.0 M HNO3 at 40°C

Explanation:

Rate of chemical reaction: This can be defined as the number of moles of reactant, converted or product formed per unit time.

Factors that affect rate of chemical reaction:

(a) Temperature:  Generally, an increase in temperature increase the rate of chemical reaction by (1) increasing the number of particles with energy equal to or greater than the activation energy, (2) Increasing the average speed of all the reactant particles, due to greater kinetic energy, leading to higher frequency of collision.

(b) Concentration: An increase or decrease in the concentration of the reactant will  result to a corresponding increase or decrease in the effective collision of the reactant and hence in the reaction rate.

other factors that affect the rate of chemical reaction are

(i) Nature of the reactant

(ii) Surface area of reactant

(iii) presence of light

(iv) presence of catalyst.

From the question above,

The condition with the highest temperature and concentration will produce the GREATEST reaction rate.

And that is  1.0 M HNO3 at 40 °C

Answer:

The count rate at the end of four days will be 7.5 counts per minute.

Explanation:

First it is important to know that half-life is the time to a piece of radioactive material to decay 50%. So if we know we start with 120 counts per minute and we already know the half-life of the isotope is 1 hour we expect that past 1 hour the material decays 50% (it's halved) so we will count 60 counts per minute, now if we wait another hour 60 counts will decay in to 30 counts per minute and so on. That should be translate to a math equation as:

final counts = initial counts * [tex](\frac{1}{2})^{\#half\,life\,periods}[/tex]

After 4 days we have 4 half-life periods passed so:

final counts= 120 counts per minute * [tex](\frac{1}{2})^{4}[/tex]

final material = 7.5 counts per minute

Answer:

a) 4.40 s

b) 2.20 s

Explanation:

Given parameters are:

At constant power  ,

initial speed of the car, [tex]v_0=0[/tex]

final speed of the car, [tex]v=32[/tex] mph

At full power,

initial speed of the car, [tex]v_0=0[/tex]

final speed of the car, [tex]v=64[/tex] mph

a)

At constant power, [tex]KE = \frac{1}{2} mv^2[/tex]

At full power, [tex]KE = \frac{1}{2} m(2v)^2[/tex]

So [tex]KE_f = 4KE_i[/tex]

So, time to reach 64 mph speed is 4 times more than the initial time

[tex]t = 4*1.10 =4.40[/tex] s

b)

[tex]v=v_0+at\\a=\frac{v-v_0}{t}=\frac{32-0}{1.1/3600}=104727.27[/tex] [tex]miles/hours^2[/tex]

For final 64 mph speed,

[tex]v=v_0+at\\t=\frac{v-v_0}{a}=\frac{64-0}{104727.27} = 6.111*10^{-4}[/tex] [tex]hours[/tex] = [tex]6.111*10^{-4}*3600=2.20[/tex] s