A swimmer who can swim in still water at a speed of 4km/h is swimming in a river. the river flows at a speed of 3km/h. calculate the speed of the swimmer relative to the river bank when she swims:- 1. downstream 2.upstream​

A 0.842g sample of Hydrogen-3 decays to 0.0526g. Approximately 4.206 half-lives have occurred.

To determine the number of half-lives that have occurred, we can use the decay equation and the concept of exponential decay. The decay equation for radioactive decay is given by:

N(t) = N₀ * (1/2)^(t/T),\((1/2)^(^t^/^T^),\)

where N(t) is the remaining amount of the substance at time t, N₀ is the initial amount, t is the time elapsed, and T is the half-life of the substance.

In this case, we have an initial mass of 0.842g (N₀) and a remaining mass of 0.0526g (N(t)). We can set up the equation as follows:

0.0526g = 0.842g \(* (1/2)^(^t^/^1^2^.^3^2)\),

where t represents the number of half-lives that have occurred.

To solve for t, we can take the logarithm of both sides of the equation:

log(0.0526g/0.842g) = log\([(1/2)^(^t^/^1^2^.^3^2^)\)].

Using the logarithmic property log(\(a^b\)) = b*log(a), we can rewrite the equation as:

log(0.0526g/0.842g) = (t/12.32) * log(1/2).

Simplifying further:

log(0.0526g/0.842g) = (t/12.32) * (-log2),

where log2 is the logarithm base 2.

Now, we can solve for t:

t = (12.32 * log(0.0526g/0.842g)) / (-log2).

Using the given values and performing the calculation, we find:

t ≈ 4.206.

Therefore, approximately 4.206 half-lives have occurred.

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Answer:

U Can check it out

Explanation:

the wire wound in a form of loop forms a coil or solenoid .when an electric current is passed through a coil or solenoid the resultant magnetic field is similar to that of a bar magnet .One end of the solenoid is North N-pole and other is S-pole like bar magnet .Since the field lines cannot cross each other, the Field lines are packed closer together inside. Therefore the field is stronger and uniform inside and weaker outside the coil.

If the wave slows down with no change in frequency, the wavelength decreases.

A wave is defined as the disturbance that has the ability to transfer energy from one point to another in a medium.

The properties of a wave include the following:

When there is a change in the speed of the wave with no change in frequency, the length of the wave would decrease.

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Answer: The answer is 120

Explanation:

Answer:

A True because only concave mirrors can produce real images

B.True because only concave mirrors can produce real images

C. Very false because a convex mirror can not produce a magnified image so a right up image of it Will always be minified

D. Very true

E. false because it will always form a virtual erect image no matter the object is placed

F. false because if an object is at center of of concave mirror the image will be real and same size as object

Block A is moving at around speed is 7.91 m/s right before it hits the ground.

The ball's parabolic motion causes it to move at a speed of 26.3 m/s right before it strikes the ground, which is faster than its straight-downfall velocity of 17.1 m/s.

Now, let's calculate the system's potential energy when collar C is removed:

PE = mgh

where

m = 4 kg (mass of block A)

g = 9.81 m/s² (acceleration due to gravity) (acceleration due to gravity)

h = 0.6 m (height that block A is raised)

PE = 4 kg × 9.81 m/s² × 0.6 m

PE = 23.54 J

Let's now find the kinetic energy of the system just before block A hits the ground:

KE = (1/2) × m × v²

where

m = 4 kg (mass of block A)

v = the block A's speed right before impact with the ground.

KE = (1/2) × m_A × v² + (1/2) × m_B × v²

where

m_A = 4 kg (mass of block A)

m_B = 5 kg (mass of block B)

d_total = d_A + d_B

where

d_A = 0.6 m (distance that block A moves)

d_B = 1 m (distance that block B moves)

d_total = 0.6 m + 1 m

d_total = 1.6 m

PE = KE

mgh = (1/2) × m_A × v² + (1/2) × m_B × v²

Substituting the known values, we get:

4 kg × 9.81 m/s² × 0.6 m = (1/2) × 4 kg × v² + (1/2) × 5 kg × v²

14112 J = (4.5 kg) × (1/2) × v²

v² = 62.693 m²/s²

v = 7.91 m/s.

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The approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

To approximate the heat transfer through the air layer in the double-paned window, we can assume that the glass layers have a negligible impact on the heat flow. The heat transfer can be calculated using Fourier's Law of Heat Conduction, which states that the heat flow (Q) is proportional to the temperature difference (ΔT) and inversely proportional to the thickness (L) and thermal conductivity (k) of the material.

First, we need to calculate the effective thermal conductivity of the air layer due to its thickness and the thermal conductivity ratio between air and glass. Let's denote the thermal conductivity of air as k_air and the thermal conductivity of glass as k_glass. Since glass has a thermal conductivity roughly 36 times greater than air, we have k_glass = 36 * k_air.

Next, we calculate the effective thermal conductivity of the air layer as:

k_eff = (k_air * L_air) / (L_air + k_glass)

Substituting the given values, we have:

k_eff = (k_air * 0.0165 m) / (0.0165 m + 0.005 m) = 0.01309 * k_air

Now, we can calculate the heat flow per second through the air layer using the formula:

Q = (k_eff * A * ΔT) / L_air

Substituting the given values, we get:

Q = (0.01309 * k_air * 0.760 m^2 * 23.0 K) / 0.0165 m = 24.4 J/s

Therefore, the approximate heat transfer through 1.65 cm of air with a temperature difference of 23.0 °C is approximately 24.4 J/s.

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Answer:

the initial velocity of the  ball is 17.14 m/s

Explanation:

Given;

maximum height reached by the ball, h = 15 m

let the initial velocity of the ball = u

at maximum height, the final velocity of the ball is zero, v = 0

The initial velocity of the ball is calculated by using the following upward motion kinematic equation;

v² = u² - 2gh

0 = u² - 2(9.8 x 15)

u² = 294

u = √294

u = 17.14 m/s

Therefore, the initial velocity of the  ball is 17.14 m/s

Answer:

F= (34) × 4.5 = 153 N

25.10 or 24.6m/s both answers are correct

Explanation:

firstly , divide the multiply with 2 and divide the result by acceleration due to gravity which is 9.8m/s or 10m/s

123*2=246

246/9.8 or 10

= 25.10 or 24.6m/s

When an object is thrown at an angle from the horizontal, the path followed by the body is called the projectile motion. The duration in seconds that the object is above the height of 14 m is 4.698 s.

Speed is the time rate at which velocity is changing.

Vertical speed component is

V₀y = 52sin 30°= 26 m/s

Given is the height h=14m

Using second equation of motion,

S=ut+ 1/2 at²

Substituting the values, we get

14 = 26t - 4.9t²

4.9t² - 26t +14 =0  

Solving the quadratic equation, we get the time as

taking the positive sign, t =4.698 s

taking the negative sign , t = 0.6082 s

Thus, the duration in seconds that the object is above the height of 14 m is 4.698s.

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The total charge in the circuit is 240 microcoulombs.

To calculate the total charge in a series circuit with capacitors, we need to use the formula Q = CV, where Q represents the charge, C is the capacitance, and V is the voltage.

In this case, we have three capacitors connected in series with capacitances of 4 μF, 3 μF, and 2 μF, respectively. The voltage across the circuit is 260 V.

To find the total capacitance (C_total) in a series circuit, we use the reciprocal rule: 1/C_total = 1/C1 + 1/C2 + 1/C3. Plugging in the values, we get 1/C_total = 1/4 + 1/3 + 1/2.

Simplifying this equation gives us 1/C_total = (3 + 4 + 6)/12 = 13/12. Taking the reciprocal, we find C_total = 12/13 μF.

Now, we can calculate the total charge (Q_total) using Q = C_total × V. Substituting the values, we get Q_total = (12/13) μF × 260 V.

Calculating the numerical value, Q_total = (12/13) × 260 = 240 μC (microcoulombs).
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Answer:

The formulas are down below

Explanation:

\(w = \frac{o}{t} \)

From V=rw

\(w = \frac{v}{r} \)

Answer:

Part a) acceleration is: 1000 \(\frac{m}{s^2}\)

Part b) time is : 0.001 second

Explanation:

Part a)

Notice that they don't give you information about time in the description of the take-off process, so we use the kinematic equation that relates acceleration with distance and velocity, and solve for the unknown acceleration;

\(v_f^2-v_i^2= 2 * a * (x_f-x_i)\)

which for our case becomes:

\(v_f^2-v_i^2= 2 * a * (x_f-x_i)\\(1\,\frac{m}{s})^2-0=2*a*(0.0005\,\,m )\\a =\frac{1}{0.001} \,\frac{m}{s^2}\\a=1000\,\frac{m}{s^2}\)

notice that we have converted the distance from mm into meters to be in agreement with the velocity units.

Part b)

we now use the definition of acceleration as the change in velocity over time to find the requested time:

\(a=\frac{v_f-v_i}{t} \\t=\frac{v_f-v_i}{a}\\t=\frac{1-0}{1000}\, s\\t=0.001\,\,s\)

Energy is that which has the ability to cause change in matter.

Energy is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed.

So in simple definition we can say that energy is that which has the ability to cause change in matter.

Based on the given statements we can classify them as;

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The magnitude of the displacement vector refers to the length or amount of the displacement vector. Displacement is the change in position of an object. Displacement is a vector quantity, which means it has both magnitude and direction. In this question, a figure skater is gliding along a circular path of radius 3.93 m.

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To determine the angle through which the wheel rotates in 1.00 second, we can start by finding the angle covered in 0.0710 seconds and then scale it up to 1.00 second.

In 0.0710 seconds, the wheel completes 3.10 revolutions. One revolution corresponds to an angle of 360 degrees or 2π radians. Therefore, in 0.0710 seconds, the wheel rotates through an angle of:

Angle = 3.10 revolutions * 2π radians/revolution = 6.20π radians

To find the angle in 1.00 second, we can use proportional reasoning. Since the time increases by a factor of 1.00/0.0710, the angle covered will also increase by the same factor:

Angle in 1.00 second = 6.20π radians * (1.00/0.0710) = 87.32π radians

Approximately, the angle through which the wheel rotates in 1.00 second is 274.39 radians.

Therefore, the wheel rotates through an angle of approximately 274.39 radians in 1.00 second.

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Answer:

\(428.75\ \text{Hz}\)

Explanation:

\(\Delta y\) = Change in water level = \(220-180=40\ \text{cm}\)

\(\lambda\) = Wavelength

\(v\) = Speed of sound = 343 m/s

Between the points of resonance there exists \(\dfrac{1}{2}\lambda\)

\(\dfrac{1}{2}\lambda=\Delta y\\\Rightarrow \lambda=2\Delta y\\\Rightarrow \lambda=2\times 40\\\Rightarrow \lambda=80\ \text{cm}\)

Wavelength is given by

\(f=\dfrac{v}{\lambda}\\\Rightarrow f=\dfrac{343}{0.8}\\\Rightarrow f=428.75\ \text{Hz}\)

The frequency of the tuning fork is \(428.75\ \text{Hz}\).

The mass of the planet is  5.98 × 10^24 kg.

To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.

First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.

Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.

Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.

Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2

Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2

Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.

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Answer:

c

Explanation:

the gas is the reversible expanded and constant temperature until it's volume is doubled

Answer:

THE RUBBER BALL

Explanation:

From the question we are told that

      The mass of the rubber ball is \(m_r = 2 \ kg\)

      The  initial  speed of the rubber ball is  \(u = 3 \ m/s\)

      The final speed at which it bounces bank \(v - 3 \ m/s\)

      The mass of the clay ball  is  \(m_c = 2 \ kg\)

       The  initial  speed of the clay  ball is \(u = 3 \ m/s\)

       The final speed of the clay ball is  \(v = 0 \ m/s\)

Generally Impulse is mathematically represented as

       \(I = \Delta p\)

where \(\Delta p\) is the change in the linear momentum so  

       \(I = m(v-u)\)

For the rubber  is  

        \(I_r = 2(-3 -3)\)

       \(I_r = -12\ kg \cdot m/s\)

=>     \(|I_r| = 12\ kg \cdot m/s\)

For the clay ball

       \(I_c = 2(0-3)\)

        \(I_c = -6 \ kg\cdot \ m/s\)

=>    \(| I_c| = 6 \ kg\cdot \ m/s\)

So from the above calculation the ball with the a higher magnitude of impulse is the rubber ball

The speed of sound traveling in the soil depends on the type of soil.

The speed of sound traveling through soil can vary depending on the composition and density of the soil.

In general, sound travels slower through soil than through air, with typical speeds ranging from around 1000 to 4000 meters per second.

The speed of sound in the soil has been researched to have important implications for seismic surveys, which use sound waves to map underground geological structures and identify potential sources of natural resources like oil and gas.

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Answer:

The average acceleration is about 8.51 m/s

Explanation:

     We can use the formula for acceleration to solve.

a = \(\frac{velocity_{final} -velocity_{start} }{time}\)

a =  \(\frac{80-0}{9.4}\)

a =  \(\frac{80}{9.4}\)

a ≈ 8.51

The Total Work done by the gas = area under the graph on the volume axis.

Clearly, from the graph, we can see that area below the isotherm is less than the area under the straight line AB process.

On drawing multiple isotherms across AB, we can see that the temperature first increases and then decreases.

1. The work done by the gas in the process A to B exceeds the work that would be done by it if the system were taken from A to B along the isotherm.

2. In the T-V diagram, path AB becomes a part of the parabola.

3. Ongoing from A to B, the temperature T of the gas first increases to the highest value and then decreases.

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The moral condition of the world today appears to be worse than it was in the antediluvian era.

The biblical account of the flood records that the world delved into apostasy in the days of Noah so much so that God regretted the fact that he created man. Some of the evils of the antediluvian world include; sodomy, drunkenness, lewdness and several forms of immorality.

We can see that these vices that led to the destruction of the world due to moral bankruptcy in the antediluvian era is still very much prevalent in our world today. The moral condition of the world today appears to be worse than it was in the antediluvian era.

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Part (a)

For interval 0 to 5 s, the velocity of the particle increases as the time taken by particle increases.

For interval 5 s to 10 s, the velocity of particle remains constant.

For interval 10 s to 15 s, the velocity of the particle decreases.

For interval 15 s to 20 s, the velocity of particle remains constant.

For interval 20 s to 25 s, the of particle decreases with increase in time.

Part (b)

The distance travelled by the particle for first 15 seconds is equal to the area of the graph which is calculated as,

Therefore, the total distance covered by the particle for first 15 seconds is 350 m.

Part (c)

The distance covered by particle from 15 s to 25 s is calculated as.

Therefore, the distance covered by particle in interval 15 s to 25 s is 150 m.

Answer:

Explanation:

10) II

Vectors are added by putting the tail of the second at the head of the first. The result is the vector from the tail of the first to the head of the second

11) IV

Negating a vector will give it the same magnitude but opposite direction. Then treat as addition as in Q 10

12) B  any value between 3 N and 17 N

Magnitude will be 3 when the vectors are co-linear but opposite in direction.

Magnitude will be 17 when the vectors are co-linear and in the same direction.

Magnitudes between 3 and 17 will occur when the vectors are not co-linear

Answer:

each parents contributes the dad gives the seed and the mom gives the egg

Explanation:

and then you are born