The strength of the electric field at a certain distance from a point charge is represented by E. What is the strength of the electric field at twice the distance from the point charge?

a.) At twice the distance, the strength of the field is E/2.
b.) At twice the distance, the strength of the field is 2E.
c.)At twice the distance, the strength of the field is 4E.
d.)At twice the distance, the strength of the field remains equal to E.
e.)At twice the distance, the strength of the field is E/4.

The problem you would encounter is measuring the height of two different people, a tall one and a short one, and getting the same answer for both of them.

No matter WHAT we're hearing out of the White House these days, you CAN'T bend and stretch your standard measuring devices, or any other 'facts', to make them fit the thing that you're measuring.  This does not work.  You're always entitled to your own opinions, but you're not entitled to your own facts.

An elastic measuring tape should not be used to measure distance because its stretchability can lead to inaccurate and unreliable measurements.

You cannot use an elastic measuring tape to measure distance accurately because it can stretch, which would result in an unreliable measurement. The problem you may face if you use an elastic measuring tape is that the stretching of the tape will lead to incorrect measurements, especially if the distances being measured require precise and firm measurement tools. Measuring tapes are typically flexible but maintain their length without stretching to ensure that measurements are consistent. For accurate measurement of length or distance, you should select a measuring tool that is suited to the size you are trying to measure, ranging from a ruler for small items to a yardstick or a non-elastic measuring tape for larger distances.

directly proportional to its frequency

Answer:

c) Because light is packaged discretely, increasing the intensity of light will increase the number of photons hitting a metal and thus the likelihood that an electron will be ejected.

Explanation:

In the photoelectric effect, light incident with a certain frequency causes the emission of photoelectrons from the surface of a metal. This effect is explained by considering light a "package" of several quanta, called photons: each photon hits only 1 electron at time, giving all its energy to the electron. If the energy given is above the work function, then the electron has enough energy to leave the metal.

The energy given off by the photon only depends on the frequency of the light, not on the intensity, according to the formula

[tex]E=hf[/tex]

where h is the Planck constant and f the frequency.

In this model, one photon hits only 1 electron at time: this means that the intensity of light (which is a measure of the number of photons in the light) does not affect the probability  of emitting an electron from the material, because that probability depends only on the energy of the photon, which depends only on the frequency of the light.

So, statement c) is wrong.

Final answer:

The correct statement about Einstein's explanation of the photoelectric effect is that the kinetic energy of the ejected electrons is directly related to the frequency of the light.

Explanation:

In Einstein's explanation of the photoelectric effect, statement d) The kinetic energy of electrons leaving the metal does not depend on the intensity of the light because intensity only affects the numbers of light packages, not their energy, is not correct.

The correct statement is that the kinetic energy of the ejected electrons is directly related to the frequency of the light. Higher frequency photons have more energy, and when they strike the metal surface, they can transfer enough energy to the electrons to overcome the work function and eject them.

Additionally, increasing the intensity of the light does not increase the energy of the individual photons, but it does increase the number of photons hitting the metal. This can increase the number of ejected electrons, but the kinetic energy of each individual electron is determined by the frequency of the photons, not the intensity of the light.

Answer:

d.100 meters

Explanation:

The diameter of the Milky Way Galaxy is approximately 100,000 light years.

Here we are using 1 millimiter (1 mm) to represent 1 light-year (1 ly). So, we can set the following proportion:

[tex]1 mm : 1 ly = x : 100,000 ly[/tex]

and by finding x, we find the diameter of the Milky Way Galaxy in the scale used:

[tex]x=\frac{(1mm )(100,000 ly)}{1 ly}=100,000 mm = 100 m[/tex]

so the correct answer is

d. 100 meters

Final answer:

Using a scale where 1 millimeter represents 1 light-year, the diameter of the Milky Way Galaxy at 100,000 light-years translates to 100,000 millimeters, which is equivalent to 100 meters. The correct answer is (d) 100 meters.

Explanation:

The Milky Way Galaxy has a diameter of approximately 100,000 light-years. To convert light-years to millimeters, we use a scale where 1 millimeter represents 1 light-year. Therefore, the Milky Way Galaxy's diameter would be 100,000 millimeters, which can be converted to meters by dividing by 1,000 (since there are 1,000 millimeters in a meter).

100,000 millimeters / 1,000 = 100 meters. So, the diameter of the Milky Way Galaxy, when represented at a scale of 1 millimeter per light-year, is 100 meters. Hence, the correct answer is (d) 100 meters.

Answer:

A

Explanation:

The horizontal component of the resultant vector is:

x = 18 cos 70° + 15

x = 21.2

The vertical component of the resultant vector is:

y = 18 sin 70°

y = 16.9

So the angle from the positive x-axis is:

θ = atan (y/x)

θ = atan (16.9 / 21.2)

θ = 39°

Answer is A.

Answer:

894 electrons

Explanation:

The electrostatic force between the two charges is given by:

[tex]F=\frac{k q_1 q_2}{r^2}[/tex]

where we have

[tex]F=4.57\cdot 10^{-21} N[/tex] is the force

k is the Coulomb's constant

q1 = q2 =q is the magnitude of the charge on each sphere

r = 20.0 cm = 0.20 m is the distance between the two spheres

Substituting and solving for q, we find the charge on each sphere:

[tex]q=\sqrt{\frac{Fr^2}{k}}=\sqrt{\frac{(4.57\cdot 10^{-21} N)(0.20 m)^2}{9\cdot 10^9 Nm^2C^{-2}}}=1.43\cdot 10^{-16} C[/tex]

And since each electron has a charge of

[tex]e=1.6\cdot 10^{-19}C[/tex]

the net charge on each sphere will be given by

[tex]q=Ne[/tex]

where N is the number of excess electrons; solving for N,

[tex]N=\frac{q}{e}=\frac{1.43\cdot 10^{-16}C}{1.6\cdot 10^{-19}C}=894[/tex]

Using Coulomb's Law and the given values, we find that each sphere must have approximately 891 excess electrons to produce a repulsive force of [tex]4.57 \times 10^{-21} N[/tex] at a distance of 20 cm.

To solve this problem, we will use Coulomb's Law, which is given by:

[tex]F = k_e \times (q_1 \times q_2) / r^2[/tex]

Where:

Given data:

We can rearrange Coulomb's Law to solve for the charge:

Since [tex]q_1 = q_2 = q[/tex], the equation becomes:

Now, we can plug in the values:

Taking the square root of both sides, we get:

Since we need to find the number of excess electrons, we divide by the elementary charge ([tex]e = 1.6 \times 10^{-19} C[/tex]):

So, each sphere must have approximately 891 excess electrons to produce the given force of repulsion.

Answer:

When it's closest to the sun.

Explanation:

The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.

Fg = m v^2 / r

The force of gravity is defined by Newton's law of universal gravitation as:

Fg = mMG / r^2

Therefore:

mMG / r^2 = m v^2 / r

MG / r = v^2

v increases as r decreases.  So the planet is moving fastest when it's closest to the sun, also known as the perihelion.

The force of gravity acting on a planet is equal to its mass times its centripetal acceleration.

Fg = m v² / r

The force of gravity is defined by Newton's law of universal gravitation as:

Fg = mMG / r²

Therefore:

mMG / r² = m v² / r

MG / r = v²

v increases as r decreases.  So the planet is moving fastest when it's closest to the sun, also known as the perihelion.

perihelion

The fastest a planet moves is at perihelion (closest) and the slowest is at aphelion (farthest). Law 3. The square of the total time period (T) of the orbit is proportional to the cube of the average distance of the planet to the Sun (R)

The Earth is closest to the Sun, at its perihelion, about two weeks after the December solstice and farthest from the Sun, or at its aphelion, about two weeks after the June solstice. Earth is farthest from the Sun when it is summer in the Northern Hemisphere.

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    I think its B. Away from the normal because light speeds up going into a less dense substance, and the ray bends away from the normal.

Option B is the right answer!

Explanation :

When light rays travel from air into glass or from air into water, it bends towards normal. This is because the speed of light rays decrease while travelling from air into glass or water .

Cheer's ♡

Answer:

John Glenn

Explanation:

Answer:

John Glenn was the first American to orbit the Earth. The first human in space was the Soviet cosmonaut Yuri Gagarin. 

Explanation:

Hope this helps. Feel free to let me know if you need any more help :)

Answer:

move the wire loops closer

Explanation:

because the closer t they are the more concentrated the energy is in that specific area

Lisa can move the wire loops closer together to increase the strength of the electromagnet. Option C is correct.

An electromagnet is a magnet whose magnetic field is generated by an electric current. Wire coiled into a coil is used to make electromagnets.

A current flowing through the wire produces a magnetic field that is focused in the hole.

The strength of the electromagnet is increased by;

Adding further twists to the coil by wrapping it around a piece of iron and increasing the amount of electricity that flows through the coil.

Hence, option C is correct.

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Answer:

16

Explanation:

If we treat the pot as a black body, then:

q = σ T⁴ A,

where q is the heat per second radiated,

σ is the Stefan-Boltzmann Constant,

T is the absolute temperature,

and A is the surface area.

If the absolute temperature doubles, then q increases by a factor of 2⁴ = 16.

Answer:

1097.8 V/m

Explanation:

The equation that relates the intensity of an electromagnetic wave with the magnitude of the electric field is:

[tex]I=\frac{1}{2}c\epsilon_0 E^2[/tex]

where

c is the speed of light

[tex]\epsilon_0[/tex] is the vacuum permittivity

E is the peak magnitude of the electric field

In this problem, we know the intensity:

I = 1600 W/m^2

So we can rearrange the formula to find E:

[tex]E=\sqrt{\frac{2I}{c\epsilon_0}}=\sqrt{\frac{2(1600 W/m^2)}{(3\cdot 10^8 m/s)(8.85\cdot 10^{-12} F/m)}}=1097.8 V/m[/tex]

Answer:

1/2

Explanation:

The energy stored in a capacitor is given by

[tex]U=\frac{1}{2}CV^2[/tex]

where

C is the capacitance

V is the potential difference

Calling [tex]C_1[/tex] the capacitance of capacitor 1 and [tex]V_1[/tex] its potential difference, the energy stored in capacitor 1 is

[tex]U=\frac{1}{2}C_1 V_1^2[/tex]

For capacitor 2, we have:

- The capacitance is half that of capacitor 1: [tex]C_2 = \frac{C_1}{2}[/tex]

- The voltage is twice the voltage of capacitor 1: [tex]V_2 = 2 V_1[/tex]

so the energy stored in capacitor 2 is

[tex]U_2 = \frac{1}{2}C_2 V_2^2 = \frac{1}{2}\frac{C_1}{2}(2V_1)^2 = C_1 V_1^2[/tex]

So the ratio between the two energies is

[tex]\frac{U_1}{U_2}=\frac{\frac{1}{2}C_1 V_1^2}{C_1 V_1^2}=\frac{1}{2}[/tex]

Radio waves are a type of electromagnetic radiation with wavelengths between 10 m to 10,000 m. In the electromagnetic spectrum this wavelength is longer than infrared light and therefore, it goes beyond the visible spectrum.  

This type of electromagnetic waves is very well reflected in the ionosphere, the layer of the atmosphere through which they travel directly or using repeaters.  

In addition, they are very useful to transport information, being important in telecommunications. They are used not only for conventional radio transmissions but also in mobile telephony and TV.  

It should be noted that since radio signals have large wavelengths, they can be diffracted around certain obstacles, such as hills and mountain ranges, preventing the signal from reaching its destination.  

Therefore, the correct option is C.

Answer:

The magnetic field reverses direction.

Explanation:

Answer:

D The magnetic field reverses direction.

Explanation:

An electric motor works based on the principle of electromagnetic induction. It is the interaction of electric current and the magnetic field that makes a motor function.

An electric motor is a machine that will convert the electric energy to mechanical energy. In this a commutator is used to change the direction of current.

When the direction of flow of current is made to change, the magnetic field also reverses the direction.

There are different types of motors like AC motor,DC motor, Induction motor etc.

An intense solar storm COULD disrupt communications and damage the power grid. (A)

An intense solar storm may disrupt communications and damage the power grid, affecting technology-reliant services such as GPS and wireless communication, as well as increasing radiation exposure for astronauts and aircraft passengers on polar routes. Advanced warnings would allow for preventative measures to protect infrastructure and people.

An intense solar storm can have significant impacts on Earth, affecting various aspects of our technology-dependent civilization. The most accurate answer to how a solar storm might affect people on Earth is A. It could disrupt communications and damage the power grid. These storms can cause geomagnetic disturbances that induce currents capable of damaging power systems, leading to widespread outages. Furthermore, the high-energy particles and radiation from solar storms can severely affect satellites and spacecraft, leading to malfunctions in navigation, communication, and other satellite-based services. Moreover, increased radiation poses risks for astronauts and could lead to higher levels of radiation for aircraft passengers on polar routes.

Answer:

Transverse

Explanation:

There are two types of waves, depending on the direction of the oscillation:

- Transverse wave: in a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave - examples of transverse waves are electromagnetic waves

- Longitudinal wave: in a longitudinal wave, the direction of the oscillation is parallel to the direction of motion of the wave - examples of longitudinal waves are sound waves

Radio waves are a type of electromagnetic waves - consisting of oscillations of electric and magnetic field that propagate in a vacuum at the speed of light - so they are an example of transverse wave.

Answer:

B (USA TestPrep)

Explanation:

A heavy nucleus splits into two smaller nuclei is true about fission reaction.

Nuclear fission is the splitting of a heavy nucleus into two lighter ones. Fission was discovered in 1938 by the German scientists Otto Hahn, Lise Meitner, and Fritz Strassmann, who bombarded a sample of uranium with neutrons in an attempt to produce new elements with Z > 92.

Nuclear fusion, in which two light nuclei combine to produce a heavier, more stable nucleus, is the opposite of nuclear fission.

As in the nuclear transmutation reactions discussed.  the positive charge on both nuclei results in a large electrostatic energy barrier to fusion.

Therefore, A heavy nucleus splits into two smaller nuclei is true about fission reaction.

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Answer:

76.3 J

Explanation:

I'm assuming the distance of 4.60 m is along the incline, not the vertical distance from the bottom.  I'll call this distance d, so h = d sin θ.

Initial energy = final energy

Energy in spring = gravitational energy + kinetic energy + work by friction

E = mgh + 1/2 mv² + Fd

We need to find the force of friction.  To do that, draw a free body diagram.

Normal to the incline, we have the normal force pointing up and the normal component of weight (mg cos θ).

Sum of the forces in the normal direction:

∑F = ma

N - mg cos θ = 0

N = mg cos θ

Friction is defined as:

F = Nμ

Plugging in the expression for N:

F = mgμ cos θ

Substituting:

E = mgh + 1/2 mv² + (mgμ cos θ) d

E = mg (d sin θ) + 1/2 mv² + (mgμ cos θ) d

E = mgd (sin θ + μ cos θ) + 1/2 mv²

Given:

m = 1.45 kg

g = 9.90 m/s²

d = 4.60 m

θ = 29.0°

μ = 0.45

v = 5.10 m/s

Solving:

E = mgd (sin θ + μ cos θ) + 1/2 mv²

E = (1.45) (9.80) (4.60) (sin 29.0 + 0.45 cos 29.0) + 1/2 (1.45) (5.10)²

E = 76.3 J

The amount of potential energy initially stored in the spring is 49.3 J.

To calculate the amount of potential energy initially stored in the spring, we need to consider the conservation of mechanical energy. At the bottom of the slope, the initial potential energy stored in the spring is converted to a combination of kinetic energy and gravitational potential energy as the block moves up the incline. We can use the equation:

PE(initial) = KE(final) + PE(final)

Substituting the given values and using the fact that the block is moving at a constant velocity up the incline, we can solve for the initial potential energy and find that it is 49.3 J.

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Answer:

B

Explanation:

"Bunting" is when the batter lets the ball hit the bat without swinging it.

Force is mass times acceleration.  The mass of the ball is the same in both scenarios, but the acceleration is much lower when bunting than it is when hitting a grand slam, so the force is much lower.

Therefore, the answer is B.

Answer: The force is much less when bunting into the in-field.

Explanation: usually, a home run is more a technique thing than a force thing.

an example can be that, two swings with the same force, but one hits the ball with the border of the bat, and the other hits the ball with the middle, in the second case more force will be transmitted to the ball, and it will go further away (increasing in this way the probability of a home run).

Assuming that in both cases the ball is hit exactly in the same way, now the force matters. Then a ball that goes out of the field is hit with more force than one that does not go out of the field.

Then the correct option would be option B: The force is much less when bunting into the in-field.

Answer:

the volume will increase

Explanation:

if the temperature is held constant , the equation is reduced yo Boyle's  law

Answer:

The distance between interference fringes increases

Explanation:

The answer to your question is Sun.

Final answer:

The new gravitational force between the two objects will be 6400 N.

Explanation:

The gravitational force between two objects can be calculated using Newton's law of gravitation, which states that the gravitational force (F) is directly proportional to the product of the masses of the objects (M1 and M2) and inversely proportional to the square of the distance between their centers (r).

So, if the gravitational force between two objects is initially 1600 N and the masses of the objects are doubled, the new gravitational force (F') can be calculated using the equation:

F' = (2M1)(2M2)G / (r^2)

Substituting the values into the equation and simplifying, we get:

F' = 4F

Therefore, the new gravitational force will be 4 times the initial force, which is 4 * 1600 N = 6400 N.

Answer:

b. circular in shape

Explanation:

The magnetic field around a current-carrying wire forms concentric circles around the axis of the wire. In particular, the direction of the field lines can be found by using the right hand rule:

- the thumb must be placed along the direction of the current in the wire

- the other fingers, wrapped around the wire, give the direction of the magnetic field lines

The strenght of the magnetic field around the wire decreases linearly with the distance from the wire, according to the equation:

[tex]B=\frac{\mu_0 I}{2\pi r}[/tex]

where

[tex]\mu_0[/tex] is the vacuum permeability

I is the current in the wire

r is the distance from the wire

(a) 18.3 m/s

According to the law of conservation of momentum, the total initial momentum of the system must be equal to the total final momentum, so we have

[tex]p_i = p_f\\m u = (m+M)v[/tex]

where

m = 0.0240 kg is the mass of the bullet

u = 400 m/s is the initial speed of the bullet

M = 0.5 kg is the mass of the block

v is the final speed of the block+bullet together

Solving for v, we find the velocity after the collision

[tex]v=\frac{mu}{m+M}=\frac{(0.0240 kg)(400 m/s)}{0.0240 kg+0.5 kg}=18.3 m/s[/tex]

(b) 17.0 m/s

The frictional force acting on the bullet-block system is

[tex]F_f = -\mu (m+M)g[/tex]

where

[tex]\mu = 0.30[/tex] is the coefficient of kinetic friction

The acceleration due to the frictional force, therefore, will be equal to the frictional force divided by the total mass:

[tex]a=\frac{F_f}{m+M}=\-mu g = -(0.30)(9.8 m/s^2)=-2.94 m/s^2[/tex]

The system travels for a distance of

d = 8.0 m

So we can find the final velocity using the equation:

[tex]v_f^2 = v^2 + 2ad[/tex]

where

v = 18.3 m/s is the initial velocity, found at point a). Substituting,

[tex]v_f = \sqrt{(18.3 m/s)^2+2(-2.94 m/s^2)(8.0 m)}=17.0 m/s[/tex]

(c) 2.1 m

We can use again the law of conservation of momentum:

[tex](m+M) v = (m+M+M')v'[/tex]

where

v = 17.0 m/s is the initial velocity of the initial bullet+block system

M = 2.00 kg is the mass of the second block

v' is the final velocity of the system

Solving for v',

[tex]v=\frac{(m+M)v}{m+M+M'}=\frac{(0.0240 kg+0.5 kg)(17.0 m/s)}{0.0240 kg+0.5 kg+2.00 kg}=3.5 m/s[/tex]

The acceleration of the system on the rough surface is still

[tex]a=-2.94 m/s^2[/tex]

So we can find the distance covered by using again the formula used before, and requiring that the final velocity should be zero (v''=0):

[tex]v''^2 - v'^2 = 2ad\\d=\frac{v''^2-v'^2}{2a}=\frac{0-(3.5 m/s)^2}{2(-2.94 m/s^2)}=2.1 m[/tex]

a)The velocity of the combined bullet and block just after collision is 18.32 m/s. b)After sliding with friction, the velocity is 16.99 m/s, and c) after sticking to a 2.00 kg block, the combined system travels 2.13 m before stopping.

First, we need to find the velocity of the combined bullet and block system just after the collision using conservation of momentum.

(a) Using conservation of momentum:

initial momentum = final momentum

m₁ = mass of bullet , v₁= vel of bullet , m₂ = mass of block ,v₂ = final velocity

( m₁ × v₁) = (m₁ + m₂) × v₂

(0.0240 kg × 400 m/s) = (0.0240 kg + 0.500 kg) × v₂

9.6 kg×m/s = 0.524 kg × v₂

v₂ = 9.6 kg×m/s / 0.524 kg

v₂ ≈ 18.32 m/s

(b) To find the velocity after sliding with friction:

The work done by friction = kinetic energy loss , total mass = M

friction force = μ × M × g

work done by friction = friction force × distance

M = 0.524 kg

μ = 0.30

d = 8.0 m

work = μ × M × g × d

work = 0.30 × 0.524 kg × 9.8 m/s² × 8.0 m

work ≈ 12.31 J

initial kinetic energy = 0.5 × M × (v₂)²

initial kinetic energy ≈ 0.5 × 0.524 kg × (18.32 m/s)² ≈ 87.84 J

final kinetic energy = initial kinetic energy - work by friction

final kinetic energy ≈ 87.84 J - 12.31 J ≈ 75.53 J

final velocity = √(2 × final kinetic energy / M)

final velocity ≈ √(2 × 75.53 J / 0.524 kg) ≈ 16.99 m/s

(c) To find the distance traveled after sticking to the 2.00 kg block:

Using conservation of momentum:

(m₃ × v₂) = (m₃ + m₄) × V   , V = final velocity new

mass of bullet block ≈ m₃ = 0.524 kg

mass of new block = m₄ = 2.00 kg

(m₃ × final velocity found in (b))

0.524 kg × 16.99 m/s = (0.524 kg + 2.00 kg) × V

8.90 kg×m/s = 2.524 kg * V_new_final

V ≈ 3.53 m/s

Now we deal with the kinetic friction again to find the stopping distance:

work = μ × M₁ × g × d  , M₁ = new total mass

M₁ = 2.524 kg

μ = 0.30

work = 0.3 × 2.524 kg × 9.8 m/s² × d

initial kinetic energy = 0.5 × M₁ × V₁²

initial kinetic energy ≈ 0.5 × 2.524 kg × (3.53 m/s)² ≈ 15.70 J

work = initial kinetic energy

0.3 × 2.524 kg × 9.8 m/s² × d = 15.70 J

d ≈ 2.13 m

Answer:

uranium

Explanation:

it is radioactive

Answer:

Explanation:

Answer:

144 ft

Explanation:

h(t) = -16t² + 64t + 80

The maximum height is at the vertex.  We can find the vertex of a parabola using -b / (2a):

t = -64 / (2×-16)

t = 2

The vertex is at 2 seconds.  The height of the stone at this time is:

h(2) = -16(2)² + 64(2) + 80

h(2) = 144

The maximum height is 144 feet.

Final answer:

To find the maximum height that the stone reaches, calculate the vertex of the quadratic equation, which leads to a time of 2 seconds. Substituting this back into the height function h(t), we find that the stone reaches its maximum height of 144 feet above the ground.

Explanation:

To determine the maximum height the stone reaches in the given quadratic function h(t) = -16t2 + 64t + 80, we need to find the vertex of the parabola. The vertex form of a parabola is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. Since our parabola opens downward (a = -16), the vertex will represent the maximum point.

The vertex of the parabola h(t) can be found by using the formula h = -b/2a, where a and b are coefficients from the quadratic equation in the form ax2 + bx + c. In this case, a = -16 and b = 64. Plugging these values into the vertex formula, we get h = -64/(2*-16), which simplifies to h = 2 seconds. This is the time at which the maximum height is reached.

Now, we can find the maximum height by substituting t = 2 back into the original equation to get h(2) = -16(2)2 + 64(2) + 80, which equals 144 feet. Therefore, the maximum height reached by the stone is 144 feet.

Answer:

Paul B. MacCready, 81; inventor of human-powered aircraft, other innovations. Paul B. MacCready, the Caltech-trained scientist and inventor who created the Gossamer Condor -- the first successful human-powered airplane -- as well as other innovative aircraft, has died. He was 81.

Explanation:

Paul MacCready is credited with creating the first human-powered aircraft, the Gossamer Condor, which was able to follow a controlled, pre-determined course.

Paul MacCready is a renowned figure in the world of aviation. He is mainly credited with creating the first human-powered aircraft to fly a pre-determined course. This aircraft is recognized as the Gossamer Condor, a revolutionary aircraft design that not only was powered by a human but also had the ability to be controlled and maneuver in flight. MacCready's innovative work in aviation technology has greatly contributed to how we understand and approach the concept of flight in the modern day.

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Answer:

5 seconds

Explanation:

The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:

d² = x² + y²

d² = (-39 + 40t)² + (228 + 30t)²

d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²

d² = 53505 + 10560t + 2500t²

The cheetah can run a total distance of:

105 * 7 = 735

The time t at this distance is:

735² = 53505 + 10560t + 2500t²

540225 = 53505 + 10560t + 2500t²

0 = -486720 + 10560t + 2500t²

0 = -24336 + 528t + 125t²

t = 12, -16.224

t can't be negative, so t = 12.

Therefore, the cheetah can wait 5 seconds before it has to start running.

Answer:

Wait time = 5 s

Explanation:

As we know that the position vector of the antelope is given as

[tex]x = -39 + 40 t[/tex]

[tex]y = 228 + 30 t[/tex]

so here at any instant of time its distance from origin is given as

[tex]d^2 = x^2 + y^2[/tex]

so we have

[tex]d^2 = (-39 + 40t)^2 + (228 + 30t)^2[/tex]

[tex]d^2 = 53505 + 2500 t^2 + 10560 t[/tex]

now when cheetah catch the antelope then distance of cheetah and antelope from origin must be same

so distance covered by cheetah in 7 s is given as

[tex]d = 105 \times 7[/tex]

[tex]d = 735 ft[/tex]

now from the above two equation

[tex]735^2 = 53505 + 2500 t^2 + 10560t[/tex]

by solving above equation we got

t = 12 s

so Cheetah must have to waith for

[tex]\Delta t = 12 - 7 = 5 s[/tex]