A diver jumps from a high platform and stays in the air for 1 second. How high was the platform?

Answer: \(1.96\times 10^{8}\ m/s\)

Explanation:

Given

Diameter of sphere is \(d=2.6\ mm\quad \quad[r=1.3 mm]\)

Charge on the sphere is \(Q=-4.5\ nC\)

Nearest distance electron can reach to sphere is \(d=0.37\ mm\)

Here, kinetic energy of electron is converted into electrostatic energy between the two i.e.

\(\Rightarrow \dfrac{1}{2}mv^2=\dfrac{kQq}{d}\\\\\Rightarrow \dfrac{1}{2}\times 9.1\times 10^{-31}\times v^2=\dfrac{9\times 10^9\times 4.5\times 10^{-9}\times 1.6\times 10^{-19}}{(3.7\times 10^{-4})}\\\\\Rightarrow v^2=3.8491\times 10^{16}\\\Rightarrow v=1.96\times 10^{8}\ m/s\)

Thus, the initial speed of electron is \(1.96\times 10^{8}\ m/s\).

Explanation:

Yes, there are differences in the shapes of position-time graphs for uniform acceleration and uniform deceleration in different directions. Let's consider each case separately:\(\hrulefill\)

(1) - Uniform acceleration towards the positive direction:

In this case, the object is moving in the positive direction with a constant acceleration. The displacement-time graph will typically be a curve that starts from an initial position and shows a steady increase in displacement over time. The shape of the graph will depend on the specific acceleration value.

(2) - Uniform acceleration towards the negative direction:

In this case, the object is moving in the negative direction with a constant acceleration. The displacement-time graph will also be a curve, but it will show a steady decrease in displacement over time.

(3) - Uniform deceleration towards the positive direction:

In this case, the object is initially moving in the positive direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a positive slope and gradually levels off.

(4) - Uniform deceleration towards the negative direction:

In this case, the object is initially moving in the negative direction but is slowing down with a constant deceleration. The displacement-time graph will be a curve that starts with a negative slope and gradually levels off.

Solution :

From the Newton's second law of motion :

F = ma

\(a=\frac{F}{m}\)

\($\frac{dv}{dt}=\frac{F}{m}$\)

\($\left(\frac{dv}{ds} \times \frac{ds}{dt}\right)=\frac{F}{m}$\)

\($v \frac{dv}{ds} = \frac{F}{m}$\)

\($v dv =\frac{F}{m}\ ds$\)

Integrating above the expression by applying the limits :

\($\int_{v_i}^{v_f} v \ dv= \frac{F}{m} \int_0^s ds$\)

Here the diameter is s= D

\($\frac{v_f^2 - v_i^2}{2}=\frac{FD}{m}$\)

The final speed of the particle after travelling distance D is

\($v_f = \sqrt{v_i^2 + \frac{2FD}{m}}$\)

The kinetic energy of the particle of mass M is :

\($K_1=\frac{1}{2}Mv^2$\)

For M = 3M

\($K_2=\frac{1}{2}(3M)v^2$\)

     \($=3(K_1)$\)

Thus the kinetic energy increases by a factor of 3.

The work done depends on the factor and the displacement of the body. Thus, the work done remains same even though the mass increases. Hence the work down increases by factor 1.

Doppler radars work by using radio waves that bounce off objects and thus the object can be tracked.

Doppler radars work by emitting a beam of energy from an antenna known as radio waves. The energy they release when they collide with airborne objects scatters in all directions, with some of it returning directly to the radar.

The quantity of energy returned to the radar increases with object size. We can now perceive raindrops in the atmosphere because of this.

The amount of time it takes for the energy beam to be delivered and returned to the radar also gives us the object's distance.

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Answer:70.6 meters

Explanation:

Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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i) The initial deceleration of the car is -1.6 m/s² and  the time taken is 5 seconds

ii) The final deceleration is -1 m/s²

iii) The total dispalcement = 1016 m

The initial deceleration of the car is given by the formula below:

v² = u² + 2as

where;

Solving for a;

12² = 20² + 2 * a * 80

a = -1.6 m/s²

Time taken, t = v - u / a

t = 12 - 20 / (-1.6)

t = 5 seconds

Final deceleration:

a = v - u / t

a = 0 - 12 / 12

a = -1 m/s²

iii) Displacement at constant velocity = 12 * 1 * 60

Displacement at constant velocity = 720 m

Final displacement, s = ut + 0.5at²

s = 12 * 12 + 0.5 * 1 * 12²

s = 216 m

Total dispalcement = 80 + 720 + 216

Total dispalcement = 1016 m

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The initial speed of the sled at the given height is 4.85 m/s.

Apply the principle of conservation of energy;

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √2gh

where;

v = √(2 x 9.8 x 1.2)

v = 4.85 m/s

Thus, the initial speed of the sled at the given height is 4.85 m/s.

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If a rose with the genotype Yy is pale yellow in color, then there is not complete dominance for neither allele and it is a case of incomplete dominance. Nonetheless, since allele Y is for pale yellow and the hybrid has this phenotype, then it is partially dominant (pale yellow, Y, option 3).

Incomplete dominance is a genetic phenomenon in which one of the two alleles present for a given gene locus is expressed more strongly when compared to the other allele, which is called partially dominant and partially recessive alleles, respectively.

Conversely, complete dominance is due to the presence of an allele that completely masks the expression of the recessive allele in heterozygous hybrid individuals.

Therefore, with this data, we can see that incomplete dominance is associated with the expression of both alleles in the heterozygous hybrid individuals.

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Answer:

~4%

Explanation:

% = |(7.6 - 7.9)|/7.9

= 0.3/7.9 ≈ 0.04 = 4%

Answer:

a) motion is PARABOLIC, b) positive particle is accelerated towards the negative plate,  c)  x = 6.19 10⁹ m

Explanation:

This exercise looks at the motion of a positively charged particle in an electric field.

a) Since the field is vertical the acceleration in this direction is

            F = m a

the electric force is

           F = q E

we substitute

          q E = m a

           a = qE / m

the mass of the particle is m = 2.00 10-16 kg

           a = 1.6 10⁻¹⁹ 2.02 10³ / 2.00 10⁻¹⁶ kg

           a = 1,616 m / s²

on the x-axis there are no relationships because there are no forces.

Since the particle has velocities in both axes, its motion is PARABOLIC,

b) the positive particle is accelerated towards the negative plate,

The field is descending, for which the event is down

c) where  hit the particle on the x-axis

they indicate that the particle leaves the center of the negative plate, for which we will fix our reference system at this point.

Let's find the components of the initial velocity.

           sin θ = v_{oy} / v

           cos θ = v₀ₓ / v

           v_{oy} = v₀ sin θ

           v₀ₓ = v₀ cos θ

           v_{oy) = 1.02 10⁵ sin 37 = 0.6139 10⁵ m / s

           v₀ₓ = 1.02 10⁵ cos 37 = 0.8146 10⁵ m / s

Let's find the time it takes to hit the negative plate

            y = y₀I + v_{oy} t + ½ a and t2

in this case the positions are y = y₀ = 0 and the accelerations

a = - 1,616m/s2,

we substitute

            0 = 0 + v_{oy} t - ½ a_y t²

            v_{oy}= ½ a_y t

            t = 2v_{oy} / a_y

let's calculate

           t = 2 0.6139 10⁵ / 1.616

           t = 7.597 10⁴s

in this time the particle travels a horizontal distance

           x = v₀ₓ t

           x = 0.8145 10⁵ 7.597 10⁴

           x = 6.19 10⁹ m

the particle falls off the plate

Answer:

Decrease

Explanation:

Working at a constant temperature when more pressure is exerted, the volume decreases.

This is known as Boyle's law.

 According to Boyle's law;

       "the volume of a fixed mass of a gas varies inversely as the pressure changes, if the temperature is constant".

  Mathematically;

          P₁V₁  = P₂V₂

P and V are pressure and volume

1 and 2 are initial and final states.

For a spacecraft is traveling with a velocity of Vox-5690 m/s:

To solve this problem, use the equations of motion to calculate the final velocity and the vertical component of the velocity. Assume that the initial velocity in the y-direction is zero.

Given:

Initial velocity in the x-direction (V₀ₓ) = -5690 m/s

Time of engine firing (t) = 865 s

Acceleration in the x-direction (ax) = 1.45 m/s²

Acceleration in the y-direction (ay) = -8.66 m/s²

(a) To calculate the final velocity (v), use the equation:

v = V₀ₓ + ax × t

Substituting the values:

v = -5690 m/s + 1.45 m/s² × 865 s

v = -5690 m/s + 1254.25 m/s

v ≈ 685.25 m/s

Therefore, the final velocity (v) is approximately 685.25 m/s.

(b) To calculate the vertical component of the velocity (vy), use the equation:

vy = ay × t

Substituting the values:

vy = -8.66 m/s² * 865 s

vy = -7484.9 m/s

Therefore, the vertical component of the velocity (vy) is -7484.9 m/s.

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Answer:

- They need oxygen to burn fuel

- Aerodynamics

- Extreme temperatures

- Radiation

- Pressure issues

Explanation:

A airplane is a heavier-than-air aircraft kept aloft by the upward thrust exerted by the passing air on its fixed wings and driven by propellers, jet propulsion, etc.

Aeroplanes cannot travel in space for several reasons:

They need oxygen to burn fuel - Aeroplane engines rely on the oxygen in the atmosphere to burn fuel and generate thrust. In space, there is no atmosphere so there is no oxygen for the engines to work.

Aerodynamics - Aeroplane wings generate lift by interacting with the air. In space, there is no air so wings would be unable to generate any lift. Aeroplanes rely on aerodynamics to fly which does not work in space.

Extreme temperatures - In space, temperatures can range from -150 degrees Celsius to 150 degrees Celsius. Aeroplanes are designed to operate within a much narrower temperature range. The extreme cold and heat of space could damage aeroplane components.

Radiation - In space, there are high levels of radiation from the Sun and cosmic rays. Aeroplane bodies are not designed to shield against this type of radiation and it could damage electronics and affect aeroplane systems.

Pressure issues - Aeroplanes are designed to withstand air pressures at altitudes up to around 12 kilometers. In low-Earth orbit and beyond, the air pressure is essentially zero. This extreme change in pressure could cause structural damage to the aeroplane.

In summary, while aeroplanes are designed to fly through the Earth's atmosphere, they lack the key features needed to operate in the extreme environment of outer space like spaceships. Aeroplanes require things like oxygen, aerodynamics and being able to withstand changes in pressure - all of which do not exist or work the same way in space.

Explanation:

The wing is pushed up by the air under it. Large planes can only fly as high as about 7.5 miles. The air is too thin above that height. It would not hold the plane up.

Vector C = 15/4x - 13y

A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head.

Two examples of vectors are those that represent force and velocity. Both force and velocity are in a particular direction. The magnitude of the vector would indicate the strength of the force or the speed associated with the velocity.

From the question;

Vector A = 3x + 5y

Vector B = -3x + 6y

2A + 7B + 4C = 0

Substituting the vectors A and B

2(3x + 5y) + 7(-3x + 6y) + 4C = 0

6x +10y - 21x + 42y +4C = 0

Taking like terms

-15x +52y + 4C = 0

4C = 15x - 52y

Dividing both sides by 4

Vector C = 15/4x - 13y

In conclusion, our Vector C is derived by substituting in the equation given.

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The radiation that is least damaging to humans is non-ionizing radiation.

Non-ionizing radiation refers to the type of radiation that does not have enough energy to remove tightly bound electrons from atoms or molecules, thus not causing significant damage to biological tissues.

Examples of non ionizing radiation include radio waves, microwaves, visible light  and low energy ultraviolet (UV) radiation. while excessive exposure to any form of radiation can have adverse effects, non-ionizing radiation is generally considered to be less harmful compared to ionizing radiation, which includes X-rays and gamma rays.

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Circular disc's moment of inertia around axis passing through mass and parallel to disc Icm=MR22

The phrase "moment of inertia" in physics refers to the precise calculation of a body's inertia with respect to rotation, or the resistance a body exhibits when a torque is applied to alter its rate of rotation around an axis (turning force).

It is a broad (additive) property: the moment of inertia for a point mass is equal to the mass squared by the perpendicular distance from the axis of rotation. Because it resists rotational motion, the moment of inertia is referred to as such and not as a moment of force.

Moment of inertia is the propensity of an object to continue rotating at a constant speed or in a condition of rest. More torque is needed to shift this state the higher the moment of inertia.

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v = s/t

44 m/s = 3.5 m/t

t = 3.5 m : 44 m/s

t = 0.08 s

a = v/t

a = 44 m/s/0.08 s

a = 550 m/s²

a : g = 550 m/s² : 10 m/s²

a : g = 55 : 1

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Answer:

981

Explanation:

100*9.81

The volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

The volume of the tire is the measure of the product of area and thickness of the tire.

The volume of the tire is calculated as follows;

Radius of the tire = 0.5 x 26" = 13"

Volume of the tire = Area x thickness

Volume of the tire = πr² x h

where;

Volume of the tire = π(13)² x (2.125)

Volume of the tire =  1,128.2 cubic inch

Thus, the volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

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Answer:

The characteristics that determine how easily two substances change temperature are:

The volume and density of the substances and the amount of time they are in contact do not directly affect how easily they change temperature.

Explanation:

Answer:

I feel like static electricity is happening when we touch objects in our home

At pH = 8, the ratio of H+ ions to OH- ions is 1:1, indicating a neutral solution. The concentration of H+ ions and OH- ions is approximately 1 x 10^(-8) mol/L. The calculated and approximated ratios should match.

To calculate the ratio of H+ ions to OH- ions at pH = 8, we need to use the relationship between pH and the concentration of H+ ions. The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution based on the concentration of H+ ions.

The formula to calculate the concentration of H+ ions (\(C_H\)+) from pH is:

\(C_H\)+ = \(10^(^-^p^H^)\)

Substituting pH = 8 into the formula:

\(C_H\)+ = \(10^(^-^8^))\)

Using the properties of logarithms, we can calculate the concentration of H+ ions:

\(C_H\)+ ≈ 1 x \(10^(^-^8^))\) mol/L

According to the concept of neutrality in water, the concentration of H+ ions is equal to the concentration of OH- ions. Therefore, the concentration of OH- ions (\(C_O_H\)-) is also approximately 1 x \(10^(^-^8^))\)mol/L.

To calculate the ratio of H+ ions to OH- ions, we divide the concentration of H+ ions by the concentration of OH- ions:

Ratio = \(C_H\)+ / \(C_O_H\)-

Ratio = (1 x \(10^(^-^8^))\) / (1 x \(10^(^-^8^))\))

Ratio = 1:1

The ratio of H+ ions to OH- ions at pH = 8 is 1:1, indicating a neutral solution. This means that the concentration of H+ ions is equal to the concentration of OH- ions, resulting in a balanced ratio.

When comparing the calculated ratio of 1:1 to the approximated ratio at pH = 8, they should be the same because the ratio of H+ ions to OH- ions is determined solely by the pH value, which is consistent and mathematically derived. Therefore, the approximated and calculated ratios should match.

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According to the diagram the equivalent resistance of the group is

40.05 ohms

The equivalent resistance is calculated by investigating the diagram to note that R2 and R3 are in parallel and both are in series to R1

Resistors in parallel is solved by

Resistors in parallel = 1/25.4 + 1/70.8

Resistors in parallel = 0.0535 ohms

Equivalent resistance

Equivalent resistance = Resistors in parallel + Resistor in series

Equivalent resistance = 0.0535 + 40

Equivalent resistance = 40.0535

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The length of the pool will be the distance travelled by the swimmer.

Distance is movement of the object with no respect to direction. To calculate distance of a moving object we should know speed and the time that the object takes.

Hence the formula to calculate distance is

D= speed × time

As above we discussed

D= speed ×time

Thus, we know speed is 2.5m/s

Time is 20 seconds

Hence D = 2.5 × 20

= 50 meters

Thus, the length of the pool is 50 meters.

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Answer:

Four times

Explanation:

The electrostatic force between the two charges is given by :

\(F=\dfrac{kq_1q_2}{d^2}\)

d is the distance between two charges

k is electrostatic constant

When both charges are doubled, \(q_1'=2q_1\ \text{and}\ q_2'=2q_2\), new force is given by :

\(F'=\dfrac{kq_1'q_2'}{d^2}\\\\F'=\dfrac{k(2q_1)(2q_2)}{d^2}\\\\F'=4\times \dfrac{kq_1q_2}{d^2}\\\\F'=4F\)

So, the electrostatic force between them will be four times what it was before.

Answer:

75 cm/second.

Explanation:

Formula:

Walking speed = stride length / time per step

Walking speed = 90cm/time per step

                         = 90cm/1.2 seconds (a common estimate time per step)

                         = 75cm/second.

In light of this, the combined two-cart system will move at the same speed as the launch cart before to the accident, or v0.

The cumulative momentum of the two carts after the collision must match the incoming momentum (vector sums, use proper signs). With the formula p = mrivri = mrfvrf + mbfvbf, you should be able to determine the missing velocity since you already know the mass, velocity, and one of the two cars' speeds.

The conservation of momentum, which is represented by the following:

m1v1 + m2v2 = (m1 + m2)vf

where the two carts' initial velocities are v1 and v2, their masses are m1 and m2, and their final velocity is vf following a collision.

Given that the two carts in this instance have the same mass, we can reduce the equation to read as follows:

2m*v0 = (2m)*vf

where m represents each cart's mass.

Solving for vf, we get:

vf = v0

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We divide the total distance travelled by the period of time to determine the average speed. By dividing the displacement by the time interval, we can determine the average velocity.

Average speed was measured by dividing the overall distances you travelled by the total time, whereas average velocity is determined by dividing your movement (a vectors pointing from the initial position toward your end position) by the whole time.

For instance, someone travelling at an average speed over 40 miles split by 10 mins, meaning 1 mile per minute, is travelling twenty miles to the north and afterwards 20 miles south (60 mph).

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