The planet TrES , orbiting a distant star, has been detected by both the transit and Doppler techniques, so we can calculate its density and get an idea of what kind it is. Using the method of mathematical insight 13.3, calculate the radius of the transiting plantet. The planetary transits block 2% of the star's light. The star TrES-1 has a radius of about 85% of our sun's radius.

The magnitude of the force on a square meter of sail is 15.45 N.

Calculate the pressure difference between the front and back surfaces of the sail.
The pressure difference (ΔP) can be calculated using Bernoulli's equation:
ΔP = (1/2) * density * (v_front^2 - v_back^2)

Given the density of air is 1.29 kg/m^3, front surface wind velocity is 6.3 m/s, and back surface wind velocity is 3.8 m/s:
ΔP = (1/2) * 1.29 kg/m^3 * ((6.3 m/s)^2 - (3.8 m/s)^2)

Calculate the force on a square meter of sail.
Force (F) can be calculated using the pressure difference and the area of the sail (A):
F = ΔP * A

Since we are calculating the force on a square meter of sail, the area is 1 m^2:
F = ΔP * 1 m^2

Solve for the magnitude of the force.
First, calculate the pressure difference using the values from Step 1:
ΔP = (1/2) * 1.29 kg/m^3 * ((6.3 m/s)^2 - (3.8 m/s)^2) = 15.45 kg/(m·s²)

Next, calculate the force using the pressure difference and area from Step 2:
F = 15.45 kg/(m·s²) * 1 m^2 = 15.45 N

The magnitude of the force on a square meter of sail is 15.45 N.

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To maximize efficiency in exterminating the bug, you would want to push on the middle block (block b) with the horizontal force of magnitude f on frictionless surface.

This is because pushing on the lighter block (block a) may not provide enough force to kill the bug, and pushing on the heavier block (block c) may require too much force, potentially damaging the blocks or injuring yourself.  To catch the bug between two blocks, you would want to catch it between the middle block (block b) and the heavier block (block c). This is because the heavier block will provide more force and pressure to crush the bug, while the middle block will keep the bug from escaping out the other side. Pushing on the lighter block (block a) would not provide enough force to effectively crush the bug.

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The answer  is option D) Nâ¢s2/m. This unit is used to express force and not mass.

The newton (option A), slug (option B), gram (option C), and kilogram (option E) are all units used to express mass in different systems of measurement. However, Nâ¢s2/m is the unit for momentum, which is a product of mass and velocity, and is therefore a unit of force and not mass.

The units used to express mass are B) slug, C) gram, and E) kilogram. The newton (A) is a unit of force, not mass, and D) N•s²/m is a derived unit for moment of inertia.

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The temperature of the mercury would increase by approximately 357.14°C when 100 J of heat energy is transferred to 20 g of mercury.

To calculate the temperature increase of the mercury, we need to know the specific heat capacity of mercury. The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of one unit of mass by one degree Celsius.

For mercury, the specific heat capacity is 0.14 J/g°C.

Using this value, we can calculate the temperature increase of the mercury:

First, we need to convert the mass of mercury from grams to kilograms:

20 g = 0.02 kg

Next, we can use the formula:

Q = m x c x ΔT

where Q is the heat energy transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the temperature change.

Substituting in the values we have:

100 J = 0.02 kg x 0.14 J/g°C x ΔT

Solving for ΔT:

ΔT = 100 J / (0.02 kg x 0.14 J/g°C)

ΔT = 357.14°C

Therefore, the temperature of the mercury would increase by approximately 357.14°C when 100 J of heat energy is transferred to 20 g of mercury.

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Potassium ions (K+) concentration of is high inside neurons at rest.  

This is due to the distribution of ions across the neuron's cell membrane, which is maintained by the sodium-potassium pump. The pump actively transports three sodium ions (Na+) out of the cell and two potassium ions (K+) into the cell, creating an imbalance in ion concentrations. This results in a negative charge inside the neuron, known as the resting membrane potential.

This potential is crucial for neuron function, as it allows the generation and propagation of action potentials or nerve impulses. When a stimulus reaches a certain threshold, it causes the opening of voltage-gated ion channels, leading to an influx of sodium ions and a change in membrane potential, this initiates the action potential, which travels along the neuron and eventually leads to the release of neurotransmitters to communicate with other cells. Maintaining a high concentration of potassium ions inside neurons at rest is essential for proper nervous system function. Potassium ions (K+)  concentration of is high inside neurons at rest.

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Answer: Table B is best suited for recording the data, as it lists the temperature readings at regular intervals of two minutes. This will allow for a clear and organized record of the temperature change over time, making it easier to analyze and draw conclusions from the data.

Explanation:

The velocity vector has a magnitude of 8.0 m/s and a direction of 30° N of E can be expressed in unit vector notation as 6.93 î + 4.0 ĵ.

A velocity vector with a magnitude of 8.0 m/s and a direction of 30° North of East can be expressed in unit vector notation using the components of the vector in the x (east) and y (north) directions. To do this, we need to resolve the vector into its components using trigonometry.

The x-component of the velocity vector can be found using the cosine function:
Vx = magnitude * cos(angle)
Vx = 8.0 m/s * cos(30°)
Vx ≈ 6.93 m/s

The y-component of the velocity vector can be found using the sine function:
Vy = magnitude * sin(angle)
Vy = 8.0 m/s * sin(30°)
Vy ≈ 4.0 m/s

Now that we have the components of the velocity vector, we can express it in unit vector notation using the standard unit vectors for the x and y directions, which are î and ĵ, respectively. The velocity vector in unit vector notation is:

V = Vx î + Vy ĵ
V ≈ 6.93 î + 4.0 ĵ

So, the velocity vector with a magnitude of 8.0 m/s and a direction of 30° North of East can be expressed in unit vector notation as approximately 6.93 î + 4.0 ĵ. This representation makes it easier to analyze and manipulate the vector in mathematical calculations, such as finding the resultant velocity or other vector properties.

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The radius of the planet's orbit around Vega is approximately 1.96 million kilometers

To find the radius of the planet's orbit, we can use Kepler's third law which states that the square of the period of an orbit is proportional to the cube of the radius of the orbit. We are given that the planet takes 55 earth years to complete one orbit around Vega. We need to convert this to seconds so that our units match up.
1 earth year = 365.25 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
So 55 earth years = 55 * 365.25 * 24 * 60 * 60 seconds = 1.73 * 10^{9} seconds.
Next, we need to find Vega's mass in kilograms. We are given that Vega's mass is 4.2 * 10^{30} kg (about 2.1 times our sun's mass).
Using Kepler's third law and the given information, we can set up the following equation:
(period of orbit)^{2} = (4π^2/G) * (radius of orbit)^{3}* (mass of star)
where G is the gravitational constant.
Solving for the radius of the planet's orbit, we get:
(radius of orbit)^{3} = \frac{[(period of orbit)^2 *(mass of star)] }{ [(4π^2})/G]}
(radius of orbit)^{3 }= \frac{[(1.73 * 10^{9} s)^{2} x (4.2 * 10^{30} kg)] }{ [(4π^{2}) * (6.6743 * 10^{-11} m^{3}/kg/s^{2})]}
(radius of orbit)^{3} = 3.17 * 10^{27}
radius of orbit = 1.96 * 10^{9} meters or 1.96 million kilometers
hence, the radius of the planet's orbit around Vega is approximately 1.96 million kilometers.

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The speed of the composite body (A + B) after the collision is (b) 6.0 m/s.

To solve this problem, we'll use the principle of conservation of momentum. Since object A is initially at rest, its momentum is 0. Object B has a momentum of mB * 12 m/s. After the collision, the two objects are stuck together, and their combined momentum is (mA + mB) * v. The initial and final momenta must be equal:

mA * 0 + mB * 12 = (mA + mB) * v

Since mA = mB, we can replace mA with mB:

mB * 12 = (mB + mB) * v
12 = 2 * v

Solve for v:

v = 12 / 2
v = 6 m/s

So, the speed of the composite body (A + B) after the collision is 6.0 m/s.

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The universe has three possible futures: an open universe, a closed universe, and a flat universe. The average density of matter in the universe, also known as the critical density, plays a significant role in determining which of these futures is correct because it directly affects the universe's expansion rate and overall geometry.

1. Open Universe: If the average density of matter is less than the critical density, the universe will expand forever, eventually becoming too sparse for gravitational forces to pull objects back together. This is an open universe, characterized by a negatively curved geometry.

2. Closed Universe: If the average density of matter is greater than the critical density, the universe will eventually stop expanding and contract due to the force of gravity. This leads to a closed universe, which has a positively curved geometry.

3. Flat Universe: If the average density of matter is exactly equal to the critical density, the universe will continue to expand but at a gradually slowing rate. This results in a flat universe with a geometrically flat, or Euclidean, geometry.

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The predicted period of oscillation t is approximately 0.85 seconds.where F is the force applied to the spring and x is the displacement from equilibrium. In this case, we know that the mass hanging on the spring is 3 kg, and the displacement is 0.25 meters.

We also know that the force applied to the spring is given by:

F = mg

a) To calculate the spring constant k, we can use the formula:

k = F/x

where g is the acceleration due to gravity, which is approximately 9.81 m/s^2. Therefore:

F = 3 kg x 9.81 m/s^2 = 29.43 N

Now we can use the formula for k:

k = F/x = 29.43 N / 0.25 m = 117.72 N/m

So the spring constant k is 117.72 N/m.

b) To predict the period of oscillation t, we can use the formula:

t = 2π √(m/k)

where m is the mass hanging on the spring and k is the spring constant. In this case, we can ignore the mass of the spring itself, so we use m = 3 kg. Plugging in the value of k that we found in part a), we get:

t = 2π √(3 kg / 117.72 N/m) ≈ 0.85 seconds

So ,the predicted period of oscillation t is approximately 0.85 seconds.

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When we plot the stress-strain curve for a tough material, we see a distinctive "yield point" where the material begins to deform plastically. This means that the material can withstand a lot of stress before it begins to permanently change shape. Once it does begin to deform, however, the strain increases rapidly and the curve becomes more steep. At the point of ultimate strength, the material can't withstand any more stress and will break.

Overall, the curve for a tough material tends to be more gradual and elongated than that of a brittle material, reflecting the material's ability to resist deformation and absorb energy before reaching its breaking point.

A tough material's stress-strain curve typically demonstrates its ability to absorb energy and undergo deformation before failure. The characteristic shape of this curve includes an initial linear elastic region, a plastic region, and finally, fracture. In the linear elastic region, the material obeys Hooke's Law and returns to its original shape upon unloading. The plastic region showcases the material's ductility, where permanent deformation occurs. A larger area under the curve indicates higher toughness, as the material can withstand more energy before fracturing.

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The angular momentum of hydrogen atom in a 4p state is √2 ℏ.

The angular momentum of an atom is given by,

L = ℏ [√l(1 + l)]

where ℏ is the reduced Plank's constant and l is the orbital quantum number.

1) In 4p state, the value of l is 1.

Therefore, the angular momentum of hydrogen atom in a 4p state,

L = ℏ [√1(1 + 1)]

L = √2 ℏ

2) In 5f state, the value of l is 3.

Therefore, the angular momentum of hydrogen atom in a 5f state,

L = ℏ [√3(1 + 3)]

L = 2√3 ℏ

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The absorption of a photon by an electron in a one-dimensional, infinite potential well can cause the electron to transition to a higher energy state.

In a one-dimensional, infinite potential well, the electron is confined to a specific region of space and can only occupy discrete energy levels. When a photon is absorbed by the electron, the electron gains energy equal to the energy of the photon.

If the energy of the photon is equal to the energy difference between the electron's initial energy level and a higher energy level, the electron can transition to the higher energy level.

This transition results in the absorption of the photon and an increase in the electron's energy. The probability of this transition occurring is determined by the selection rules for the system, which depend on the properties of the photon and the system's geometry.

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Answer:

B. A large force produces a large change in the object’s momentum only if the force is applied over a very short time interval.

Explanation:

This statement aligns with Newton's second law of motion, which states that the change in momentum of an object is directly proportional to the force applied and occurs in the direction of the force, and is inversely proportional to the time over which the force is applied. Therefore, a large force applied over a very short time interval can result in a large change in the object's momentum, while a small force applied over a long time interval may not produce a significant change in the object's momentum.

The force exerted by a spring with a stiffness of 100 N/m that was compressed by 0.02 m can be calculated using the formula F = kx.

where F is the force in newtons, k is the stiffness in newtons per meter, and x is the compression or extension in meters.

Substituting the given values, we get:

F = 100 N/m x 0.02 m
F = 2 N

Therefore, the force exerted by the spring is 2 N.

To find the force exerted by a spring with a stiffness of 100 N/m that was compressed at 0.02 m, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is equal to the product of its stiffness (k) and the displacement (x) from its equilibrium position:

Force (F) = k x X

Given the stiffness (k) is 100 N/m and the displacement (x) is 0.02 m, we can plug these values into the formula:

Force (F) = 100 N/m x 0.02 m

Now, simply multiply the values:

Force (F) = 2 N

Therefore, the force exerted by the spring is 2 Newtons (N).

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To find the frequency of a 60 vibrations per second wave that travels 30 meters in 1 second, you can use the following formula:

Frequency (f) = Number of vibrations / Time

In this case, the number of vibrations is 60, and the time is 1 second.

Step 1: Plug the values into the formula:
Frequency (f) = 60 vibrations / 1 second

Step 2: Solve for the frequency:
Frequency (f) = 60 Hz

So, the frequency of the wave is 60 Hz.

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The orbital period of the outer stars in the given galaxy is approximately 5.20 x 10^14 seconds, or about 16.5 billion years.

To calculate the orbital period of the outer stars in the given galaxy, we can use the following formula:

T = 2πR / v

where T is the orbital period, R is the radius of the galaxy, and v is the velocity of the outer stars.

In this case, the velocity of the outer stars is given as 150 km/s, which we can convert to m/s:

v = 150 km/s = 150,000 m/s

The radius of the galaxy is given as 4.0 kpc, which we can convert to meters:

R = 4.0 kpc = 4.0 x 10^3 x 3.086 x 10^16 m/kpc = 1.2344 x 10^20 m

Substituting these values into the formula, we get:

T = 2πR / v = 2π(1.2344 x 10^20 m) / (150,000 m/s)

T = 5.20 x 10^14 seconds

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The magnification of the mirror after calculations is 0.99.

We can use the mirror formula and magnification formula to solve this problem:

1/f =[tex]1/d_o + 1/d_i[/tex]

magnification = -[tex]d_i/d_o[/tex]

where f is the focal length of the mirror, [tex]d_o[/tex] is the distance of the object from the mirror, and [tex]d_i[/tex] is the distance of the image from the mirror.

(a) To find the position of the object, we can rearrange the mirror formula:

[tex]1/d_o = 1/f - 1/d_i[/tex]

Substituting the given values, we get:

[tex]1/d_o[/tex] = 1/(-41.5 cm/2) - 1/20.5 cm

Simplifying, we get:

[tex]1/d_o[/tex] = -0.0482 cm^-1

Therefore:

[tex]d_o[/tex] = -20.7 cm

Note that the negative sign indicates that the object is located in front of the mirror.

Therefore, the object is located 20.7 cm in front of the mirror.

(b) To find the magnification, we can use the magnification formula:

magnification = -[tex]d_i/d_o[/tex]

Substituting the calculated values, we get:

magnification = -20.5 cm / (-20.7 cm)

Simplifying, we get:

magnification = 0.99

Therefore, the magnification of the mirror is 0.99.

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In a metal conductor, the relationship between current and voltage is typically described by Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage.

.

(V) applied across it, and inversely proportional to the resistance (R) of the conductor. Mathematically, Ohm's Law can be expressed as:

V = I * R

where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. This means that when the voltage across a metal conductor is increased, the current through the conductor will also increase, assuming the resistance remains constant. Similarly, when the voltage is decreased, the current will also decrease, again assuming the resistance remains constant. This linear relationship between current and voltage is a fundamental principle in electrical circuits and is widely used in the analysis and design of electronic systems.

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The height the ball will reach if the initial kinetic energy is double is 4 times the original height (4h).

The initial kinetic energy of the ball is given as K0, and it is related to the initial velocity v₀ by the formula [tex]K_0 = 1/2mv0^2[/tex], where m is the mass of the ball. When the ball is shot straight up, it reaches a maximum height h, which can be calculated using the formula[tex]h = v_0 {^2/2g[/tex], where g is the acceleration due to gravity.

If the initial kinetic energy of the ball is doubled, then the initial velocity of the ball will also double, since [tex]K_0 = 1/2mv0^2[/tex].

Therefore, the new initial velocity is
[tex]v_0 = \sqrt{(2K_0/m)[/tex]
[tex]= \sqrt(21/2m*v_0 ^ {2}/m)[/tex]
[tex]= \sqrt{(2)*v_0.[/tex]

Using the formula for maximum height, the new maximum height h' can be calculated as [tex]h' = v_0^2/2g = (\sqrt{(2)*v_0)^2}/2g = 2v_0^2/2g = 2h.[/tex]

Therefore, the new height the ball will reach if the initial kinetic energy is double is 2 times the original height (2h), or 4 times the original height (4h) if compared to the initial height before being shot up.

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Induced current does require energy to be produced, as it involves the transfer of energy from one system to another. In the case of an induced current, the energy required to produce the current comes from the original source of the changing magnetic field.

In case 2, where energy conservation seems to be violated, it is likely that the system is not closed, and energy is being transferred into or out of the system.

When an induced current is generated, it requires energy. This energy comes from an external source, such as a changing magnetic field, which causes the electrons in the conductor to move, creating the current. The energy conservation principle states that energy cannot be created or destroyed, only converted from one form to another.

In case 2, the energy for the induced current comes from a decrease in kinetic energy (KE) or an increase in gravitational potential energy (PE). When there is less KE, more energy is available to be converted into the induced current.

Conversely, when there is more gravitational PE, this energy can be converted into electrical energy for the induced current. So, induced current does need energy, and this energy comes from either a decrease in KE or an increase in gravitational PE, ensuring that energy conservation is maintained.

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The maximum instantaneous power consumption of the 120 V AC microwave oven that draws 8.5 A is 1.02 kW

The maximum instantaneous power consumption of the microwave can be calculated using the formula

P = VI, where P is power in watts, V is voltage in volts, and I is current in amperes.

Therefore, the maximum instantaneous power consumption of the microwave can be calculated as follows:
P = 120 V x 8.5 A = 1020 watts
To convert wats to kilowatts, we divide by 1000, so the maximum instantaneous power consumption of the microwave in kilowatts is:
P = 1020 watts / 1000 = 1.02 kW

Hence, the maximum instantaneous power consumption of the 120 V AC microwave oven that draws 8.5 A is 1.02 kW, which can be calculated using the theory of power being equal to voltage multiplied by current.

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A feather and a coin will have equal accelerations when falling in a vacuum because the force of gravity is the same for each object, regardless of their weight or mass.

In a vacuum, there is no air resistance or friction to slow down their fall, so they will both experience the same gravitational pull towards the Earth. This is why their velocities will also be the same as they fall towards the ground. The ratio of each object's weight to its mass does not affect its acceleration in a vacuum, as the force of gravity is the only factor at play.

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The statement "Two free (not held fixed) point charges q and 4q are a distance l apart. A third charge is placed such that all three charges have zero acceleration" is true.

A third charge can be placed such that all three charges have zero acceleration. To achieve this, the third charge should be placed along the line connecting the two initial charges, closer to the charge with the smaller magnitude (q). The magnitude of the third charge will be equal to the square root of the product of the magnitudes of the two initial charges, i.e., √(q × 4q) = √(4q²) = 2q. The sign of the third charge will be opposite to the charge of q, as it needs to provide equilibrium to both charges.

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The blue star is hotter than the red star. The color of a star is an indication of its temperature.

Stars emit light across a range of wavelengths, and the peak of this distribution is determined by the star's temperature, according to Wien's Law.

Blue stars are hotter, with temperatures typically above 10,000 K, while red stars are cooler, with temperatures usually below 4,000 K. So, when comparing a red star and a blue star, it can be said with certainty that the blue star is hotter.

In the given comparison between a red star and a blue star, the only fact that can be stated with certainty is that the blue star has a higher temperature than the red star. Other factors, such as distance from Earth, proper motion, radial velocity, and mass, cannot be determined solely based on the stars' colors.

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Interstellar dust, dark nebulae, and the twinkling of stars are evidence visible to human eyes that suggest the spaces between stars are not totally empty.

Space between the stars is called the interstellar space. These spaces are not actually empty and result in some common phenomena visible to the human eye.

The presence of interstellar dust, which is made up of tiny particles that can scatter and absorb light, causes it to appear redder and dimmer than expected.

The observation of gas clouds, such as the dark nebulae appear as dark patches against the background of stars. These clouds are made up of gas and dust and can be detected through their absorption and emission of light.

Additionally, the presence of cosmic rays, which are high-energy particles that travel through space, also suggests that the space between stars is not completely empty.

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Network modifiers are elements or compounds that can alter the network structure of a ceramic glass by breaking the covalent bonds and introducing ionic bonds. The addition of network modifiers can decrease the glass transition temperature (Tg) of a ceramic glass.

Network modifiers are elements or compounds that can alter the network structure of a ceramic glass by breaking the covalent bonds and introducing ionic bonds. The addition of network modifiers can decrease the glass transition temperature (Tg) of a ceramic glass. This is because the introduction of ionic bonds disrupts the continuous network of covalent bonds, which lowers the energy required for the molecules to move and transition from a solid-like state to a liquid-like state. Therefore, the more network modifiers added to a ceramic glass, the lower the Tg will be. Conversely, the removal of network modifiers or the addition of network formers (elements or compounds that enhance the network structure) will increase the Tg of a ceramic glass.

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The diver will hit the water after 9/4 seconds.

To find the time when the diver hits the water, use the equation 16t² = 81. To find t, follow these steps:

1. Divide both sides of the equation by 16: t² = 81/16
2. Take the square root of both sides: t = √(81/16)
3. Simplify: t = 9/4 seconds


To calculate the velocity of the diver when they hit the water, use a = 9/4 seconds. The distance when the diver hits the water is d(a) = 16(9/4)² = 81 ft.

The velocity of the diver when they hit the water cannot be determined using the given information, as the limit expression for velocity is incomplete.

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